tan theta equals 8 / 15 find sine theta + cos theta / cos theta (1 - cos theta)​

Answers

Answer 1

I guess you have to find

[tex]\dfrac{\sin\theta+\cos\theta}{\cos\theta(1-\cos\theta)}[/tex]

given that [tex]\tan\theta=\frac8{15}[/tex].

We can immediately solve for [tex]\sec\theta[/tex]:

[tex]\sec^2\theta=1+\tan^2\theta\implies\sec\theta=\pm\dfrac{17}{15}[/tex]

(without knowing anything else about [tex]\theta[/tex], we cannot determine the sign)

Then we get [tex]\cos\theta[/tex] for free:

[tex]\cos\theta=\dfrac1{\sec\theta}=\pm\dfrac{15}{17}[/tex]

and we can now solve for [tex]\sin\theta[/tex]:

[tex]\sin^2\theta+\cos^2\theta=1\implies \sin\theta=\pm\dfrac8{17}[/tex]

Notice that we have 2*2 = 4 possible choices of sign for either sin or cos.

• If both are positive, then

[tex]\dfrac{\sin\theta+\cos\theta}{\cos\theta(1-\cos\theta)}=\dfrac{391}{90}[/tex]

• If both are negative, then

[tex]\dfrac{\sin\theta+\cos\theta}{\cos\theta(1-\cos\theta)}=\dfrac{391}{480}[/tex]

• If sin is positive and cos is negative, then

[tex]\dfrac{\sin\theta+\cos\theta}{\cos\theta(1-\cos\theta)}=\dfrac{119}{480}[/tex]

• If cos is positive and sin is negative, then

[tex]\dfrac{\sin\theta+\cos\theta}{\cos\theta(1-\cos\theta)}=\dfrac{119}{30}[/tex]


Related Questions

Identify the binomial

Answers

Step-by-step explanation:

where are the numbers?

Question 5 (1 point)
A rectangle has a length of x + 7 and a width of x - 2. Write an
equation that describes the area, A, of the rectangle in terms of
Ob
A = 2x + 5
A = x2
+ 9x - 14
A = 2x + 9
ос
Od
A=x²+.
= x + 5x – 14

Answers

Answer:

A = x^2 + 5x - 14

Step-by-step explanation:

A = L × W

A = (x+7) × (x-2)

A = x^2 + 7x - 2x - 14

which number line represents the solution to -2X equals 4​

Answers

Answer:

It is B

Step-by-step explanation:

-5(x+2)+3x= Which expression can be written in the box on the other side of the equation

Answers

Answer:

O-2(x+5)

Step-by-step explanation:

I have to much time on my hands

Answer:

-2x-10

Step-by-step explanation:

-5(x+2)+3x=

Distribute

-5x-10 +3x

Combine like terms

-2x-10

True statement about parallelogram

Answers

All four sides are congruent.

Answer:

a parallelogram is a simple non-self-intersecting quadrilateral with two pairs of parallel sides.

Step-by-step explanation:

2 ton of rocks cost $2,920.00. What is the price per pound?

Answers

Answer:

$0.73 per pound

Step-by-step explanation:

2920 divided by 4000 (2 tons is 4000 pounds) equals 0.73

a(x+y)-a(x-y) simplified .

Answers

Answer:

2ay

Step-by-step explanation:

a(x+y)-a(x-y)

Distribute

ax +ay - ax + ay

Combine like terms

2ay

Answer:   2ay

Work Shown:

a(x+y)-a(x-y)

ax+ay-ax+ay

(ax-ax)+(ay+ay)

(0ax)+(2ay)

0+2ay

2ay

Suppose the dimensions of your dining room are 12 feet by 14 feet. You purchase a rectangular table that is 7 feet by 9 feet. After you put the table in the dining room, how much space is left in the dining room (in square feet)?

Answers

7 x 9 = 63

12 x 14 = 274

add them together and you gey the total space left

Solve the equation 7 minus 2X equals 19

Answers

Answer: x=-6

Step-by-step explanation:

Answer:

x=-6

Step-by-step explanation:

Put it in an equation,

7-2x=19

Solve for x

Subtract 9 on both sides

-2x=12

Divide -2 on both sides

x=-6

NEED HELP GIVING 20 POINTS

Answers

Answer:

-5

Step-by-step explanation:

Just substitute the values and use a calculator to solve.

Round 3528003 to the nearest million

Answers

Answer:

it would be rounded to about 4028003

Step-by-step explanation:

Answer:

4,000,000

Step-by-step explanation:

10.2 is 21.25% of what number?​

Answers

Answer: 48

Step-by-step explanation: Using proportions

48 is the number whose 21.5 percent is 10.2 .

What is percentage?

A percentage is a number or ratio that can be expressed as a fraction of 100.

How to convert a percentage into a number?

Divide the given percentage by hundred to convert it into a number.

Let x be a number whose 21.5% is 10.2.

Therefore,

[tex]\frac{21.25}{100} (x) = 10.2[/tex]

⇒ [tex]21.25x = 10.2(100)[/tex]

⇒[tex]21.25x = 1020[/tex]

⇒[tex]x = \frac{1020}{21.25}[/tex]

⇒[tex]x = 48[/tex]

Hence, 48 is the number whose 21.5 percent is 10.2.

Find out more about percentage here:

https://brainly.com/question/13450942

#SPJ2

Please help quick
Divide polynomials using long division
(13q–91)÷(q–7)

Answers

Answer:

13

Step-by-step explanation:

q-7 can go into 13q-91 thirteen times.

Set up the long division sign with the q-7 on the outside and the 13q-91 inside.

Then, notice that to get to 13, you multiply the q and 7 by 13. This gets both terms to 13q and 91, which cancel out the numbers inside the long division sign.

What does the grid represent

Answers

Answer:

0.030

Step-by-step explanation:

I don't really know how to explain this one, sorry.

Hope this helps! (✿◕‿◕✿)

[tex]\tt Step-by-step~explanation:[/tex]

We have to find out what the shaded regions represent. We can count up ten rectangles in total, and three of them are shaded. We take the amount of shaded rectangles over the total amount to get [tex]\tt \frac{3}{10}[/tex] as a fraction, and 0.3 as a decimal.

[tex]\tt First~option:[/tex]

The first choice is 0.300. The zeroes at the end of the number do not mean anything, so we can simplify it to 0.3. 0.3 is equal to 0.3, so this is not the answer.

[tex]\tt Second~ option:[/tex]

The second choice is 0.30. Again, we can simplify it to 0.3. We can see that it is equivalent to 0.3, so this is not the answer, either.

[tex]\tt Third~option:[/tex]

Our third choice is 0.3. 0.3 = 0.3, so this is not our answer either.

[tex]\tt Fourth ~option:[/tex]

Our final choice is 0.030. Take out the last zero to get 0.03. 0.03 is equal to [tex]\tt \frac{3}{100}[/tex], so this is our answer, since it is not 0.3.

[tex]\large\boxed{\tt Our ~final~answer:~Last~option:~0.030}[/tex]

Find the value of x in each case:

Answers

Answer:

KLP=54, LPM=18, PMN=108

Step-by-step explanation:

x+3x+2x+72=180

6x=108

x=18

3x=54

x=18

2x+72=108

The regular price of a color tv is 559.45. during a sale, hill tv is selling the tv for 457.41. Determine the percent decrease in the price of the tv.

Answers

Answer:

478

Step-by-step explanation:

559.45-457.41=102.04

102.04/559.45*100

approximately 478

Tim read 70% of his book containing 230 pages how many pages does he have left

Answers

Hello!

Considering the whole book as 100%, there’s 30% left.

Then, 30% of 230 = 0,3*230 = 69 pages.

Hope you’re all right! Stay safe!

69 Pages are left to read by Tim.

What is Unitary Method?

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Total pages= 230

Percentage of reading = 70%

So, number of Pages Tim reads

= 70 /100 x 230

= 161 pages

Hence, number of pages left = 230- 161 = 69 pages

Learn more about Unitary Method here:

https://brainly.com/question/22056199

#SPJ2

Solve for a. 3(a+3)+6=30

Answers

Answer:

a = 5

General Formulas and Concepts:

Order of Operations: BPEMDAS

Properties: Distributive, etc.

Step-by-step explanation:

Step 1: Write equation

3(a + 3) + 6 = 30

Step 2: Solve for a

Distribute 3:                                  3a + 9 + 6 = 30Combine like terms:                     3a + 15 = 30Subtract 15 on both sides:           3a = 15Divide 3 on both sides:                a = 5

Step 3: Check

Plug in a to verify it's a solution.

Substitute:                                   3(5 + 3) + 6 = 30Add:                                             3(8) + 6 = 30Multiply:                                       24 + 6 = 30Add:                                             30 = 30

The string is 30 centermeters long how long is string in inches

Answers

Answer:

11.811 inches

Step-by-step explanation:

every inch is 2.54 centimeters

Answer:

11.811 inches

Step-by-step explanation:

divide the length value by 2.54

help help help help help help

Answers

Answer:

no, its an acute triangle

Step-by-step explanation:

Answer:

This is not a right triangle

Step-by-step explanation:

The reason as to why this is a right triangle is because I used the equation a2 + b2 = c2.    * = 2

24* + 42*= 2340

26*= 676

2340 is not the same as 676

Therefore the triangle is not a right triangle

At Supply World, 4 pens cost $10.00. How much do 3 pens cost if the price per pen is the same

Answers

If you divide 4 by 10 you get 2.5. Multiple by 3 and the answer would be 5.5-
Hope this helps

Answer: $7.50

Step 1: Divide.

10 ÷ 4 = 2.50

Step 2: Multiply.

2.50 × 3 = 7.50

The answer is 7.50

Janice is roller skating at a constant speed away from her house. The first half of the street is flat, but the second half has a steep upward hill. Janice moves more slowly as she skates up the hill.

Which graph shows Janice's position as she roller skates away from her house?

A. Z
B. X
C. W
D. Y​

Answers

Answer:

It's Z.

Step-by-step explanation:

Because the road is straight at first, then it gets steep.

which means that the road goes down,

kinda like a drop off.

Answer:

Y moving quicker, then moving slower rate

Answer the following question. What is 6x-7-12x+3?

Answers

Answer:

-6x-4

Step-by-step explanation:

Combine 6x and −12x to get −6x.

−6x−7+3

Add −7 and 3 to get −4.

−6x−4

Answer:

-6x-4

Step-by-step explanation:

6x-12x

-6x

-7+3

-4

-6x-4

sin θ=√5/3, cos θ=2/3

3/2

2√5/5

√5/2

3√5/5

Answers

9514 1404 393

Answer:

  cos θ = 2/3

Step-by-step explanation:

We presume you want the value of the cosine for

  sin θ = √5/3 ≈ 0.745356

__

There are several possible approaches you can take to this problem.

1) Using the trig identity:

  cos = √(1 -sin²)

  cos θ = √(1 -(√5/3)²) = √(1 -5/9) = √(4/9)

  cos θ = 2/3

__

2) Another approach you can take is to use a calculator to find the angle, then use the calculator to find the cosine of the angle.

  cos θ = cos(arcsin(√5/3)) = cos(arcsin(0.745356)) = cos(48.19°) ≈ 0.666667

  cos θ = 2/3

__

3) Yet another approach is to check the answer choices for reasonableness.

You are given sin θ = 0.745356. This is more than 0.707107, the value where sine and cosine are equal, so the cosine value must be less than 0.707. The answer choices are ...

  2/3 ≈ 0.667

  3/2 . . . greater than 1; not a viable cosine value

  2√5/5 ≈ 0.894 . . . too large

  √5/2 . . . greater than 1; not a viable cosine value

  3√5/5 . . . greater than 1; not a viable cosine value

So, just looking at the values of the offered answer choices, you can choose the correct one. It is the only value with the appropriate magnitude.

  cos θ = 2/3

67 times a number minus 65 is equal to -4 less than the number

Answers

Answer:

Translation is 67x-65=x-4, you can use any variable for the number.

Step-by-step explanation:

Simplify (x^2/7)^3/4

Answers

Answer:

(x^2)^(3/4)/7^(3/4)

Step-by-step explanation:

If f(x) = 22 – 4x – 5, find the following:
a. f(-2)
b. f (10)
.c. f(0)

Answers

Answer:

a.25

b.-23

c.17

Step-by-step explanation:

Plug each value in for x and solve

The gift box is 10 cm x 12 cm x 3 cm what is the volume of the box

Answers

Answer:

volume  = L*B*H

Step-by-step explanation:

SO,

Volume of the box = L*B*H

OR, Volume of the box = 10*12*3

thus, Volume of the box =360

Circle YES or NO The terms -5x and 5x are like terms.

Answers

Answer:

YES

Step-by-step explanation:

Answer:

yes!

Step-by-step explanation:

x are still the same term whether they are negative or not! Good Luck!

Determina la ecuación de recta de una recta en su forma estándar, tal que contiene al
punto(3,-4) y es paralela a la recta que pasa por (0,2) & (3,1).​

Answers

Big the answer would be that it’s tab dfg fog hb is a day or a long day of a week or so before I can join the summer or just like me or I wanna is the day you can come over tomorrow or tomorrow I just got done and I’ll give you the money I have
Other Questions
Suppose that the grade 7 student expected to sell between 100 and 150 hotdogs. How many packages of 12 wieners and 8 buns should the students buy if they don't want any leftovers ?Justify your answer .How many packages of each should they buy if they expect to sell more than 300 hotdogs. HURRY!! THIS ASSIGNMENT IS DUE IN 5MIN!!! THANK YOU!!!!!!State whether the percent of change is a percent of increase or a percent of decrease. Then find the percent of change. original: 60, new: 75 Stuck on these couple of questions could i get help?? please help ): thank you Define physical change true or false: 1. T F Cities are usually colder than their surrounding regions. 2. T F Climate has no effect on the formation of soil. 2.T F Mangroves are a keystone species. 3. T F The brackish water of estuaries does not support a diversity of marine life. 4. T F Large browsing animals are abundant in chaparral. (O how is the igneous rock formed Describe how you have applied one of the principles of exercise in your own life. Which answer is equivalent to _36_8 Which of these is a chemical property of aluminium Terry's mother combines 1.5 liter bottles of juice with two 0.25 liter cans of sparkling water to make punch. what is the total amount of punch that Terry's mother make? Which word is the coordinating conjunction in this sentence? Math and science are my favorite subjects. A. are B. and C. my D. subjects Two stores sell CDs in packages, as shown in the table below.CD Prices at Store ANumber of CDs in Package1122045Cost$0.70$8.40?$31.50CD Prices at Store BNumber of CDs in Package1203065Cost$0.60?$18.00$39.00If the rate at each store is constant, which statement correctly compares the cost of a package containing 20 CDs?The cost at Store A is $2.00 greater than at Store B.The cost at Store B is $2.00 greater than at Store A.The cost at Store A is $1.00 greater than at Store B.The cost at Store B is $1.00 greater than at Store A. in a salad with vegetables containing 50 calories dressing is added at 100 calories per ounce. The total number of calories can be represented by the equation f(x) = 100x +50. What is the reasonable range for the situation? Read the excerpt from The People Could Fly.Now the first time the buckras run Bruh Deer with the hounds, he didn't know nothin about them. And he just lie down in his bed in the thicket on the edge of the broom-grass field. But here come the hounds, and Bruh Deer so afraid and so, he jump and he run. And he gets away to the river first. Just as he ready to jump off the bluff above the river, he look down and see Bruh Alligator's two big eyes come risin out of the water. Bruh Alligator just waitin for him!The details in this excerpt best help readers imagine what the scenesounds like.looks like.smells like.feels like. What is the approximate value of 8 to the nearest tenth? What is one of the most deaths in teensA. Car crashB. Drinking alcoholC. Doing drugsD. Fist fighting Which suggested change would cause the greatest increase in the amount of overload in your weight-training workout?A.adding more weight and increasing the distance over which the weight is movedB.decreasing the weight and the speed at which the weight is movedC.changing the type of activity you are using to give you more variety in your workoutD.keeping your current workout but dividing it up over five days instead of three A(n) ______________ is an organism that lives on another organism and causes harm to that organism complete the template below to help you plan out your letter my product its a custom can of Pringles and I made the flavor of Pringles popcornI. Paragraph one- Introduction1. (introduce yourself and explain your experience related to the product) _____________________________________________________________________2. (explain why you are writing) _____________________________________________________________________ 3. (briefly describe your food product and name for your food) _____________________________________________________________________II. Paragraph two- Describe your Food Product1. ( describe the flavors, ingredients, texture) _____________________________________________________________________2. (what does your food look like) _____________________________________________________________________3. (how is your food unique what makes it different than other products out there) _____________________________________________________________________III. Paragraph three- Describe the Packaging1. (describe the colors in your packaging )____________________________________________________________2. (describe any images, art, or photos on the package) _____________________________________________________________________3. (describe the size and materials used in the package) ______________________________________________IV. Paragraph four- Convince The Company1. (describe the target population who will buy the food (ex. Moms, diabetics, vegetarians, teens) _____________________________________________________________________2. (why should they make and market your food?)_______________________________________________________________3. (how much will you sell your food for? Sold individually or in larger quantities?) _____________________________________________________________________V. Paragraph five- Conclusion1. (Tell what you want the company to do) ___________________________________________________________________________________________________________________2. (Restate what makes your food delicious) ___________________________________________________________________3. (Restate what makes your food unique) _____________________________________________________________________