Which statement is true for all real values of theta?

Which Statement Is True For All Real Values Of Theta?

Answers

Answer 1

Answer:

  (a)  sec²(θ) -tan²(θ) = 1

Step-by-step explanation:

The identity relation between sec(θ) and tan(θ) is ...

  tan²(θ) +1 = sec²(θ)

__

When tan²(θ) is subtracted from both sides of this equation, the result matches the first choice:

  sec²(θ) -tan²(θ) = 1

_____

Additional comment

This is a variation of the "Pythagorean" relationship between sine and cosine. There is a similar relation between cot²(θ) and csc²(θ).

  [tex]\sin^2\theta+\cos^2\theta=1\\\\\dfrac{\sin^2\theta}{\cos^2\theta}+\dfrac{\cos^2\theta}{\cos^2\theta}=\dfrac{1}{\cos^2\theta}\qquad\text{divide by $\cos^2\theta$}\\\\\tan^2\theta+1=\sec^2\theta[/tex]


Related Questions

what is the volume of this cone in cubic inches

Answers

Answer:

84.78 inches cubed  - hope this helped :)

Step-by-step explanation:

formula - πr^2[tex]\frac{h}{3}[/tex]

3 x 3 x 3.14 = 28.26

28.26 x 9/3

28.26 x 3

answer = 84.78

Answer:

84.78 inches cubed

Step-by-step explanation:

You need to comprehend the volume formula for cones

Volume Formula for Cones: V=1/3hπr²


Your measurements:

9 inches for height

3 inches for radius

**Radius is half of a circle and diameter is full of the circle/base.***


Equation:V=1/3 x 9in x π x 3²

You should do 3 squared first so that you can input it into your calculator easily.

V=1/3 x 9in x π x 9


Now on a calculator do 1 divided by 3 which is the "1/3" in the formula.

Then multiply 9, 3.14 for pi, and 9 for radius.

Note: You should do 3.14 for pi not the whole pi symbol on the calculator.

Your answer: 84.78 in cubed

       

Question content area top
Part 1
An airplane on autopilot took 5 hours to travel​ 3,475 kilometers. What is the unit rate for kilometers per​ hour?

Answers

Answer:

695

Step-by-step explanation:

Am I correct? Tell Me How
The dot plot shows the number of cough drops that were in each bag of cough drops inspected at a factory.

How many bags of cough drops were inspected? Enter your answer in the box.

Answers

Answer:

yes its 18

Step-by-step explanation:

count the dots

25 points! Please help! Will give brainliest to correct answer!

Answers

Answer:

I think AC is 6.

Step-by-step explanation:

This looks like an equilateral triangle so that means because there is a 3 on  one side of the line it should be the same on the other side of the line so 3 x 2 = 6.

Step-by-step explanation:

[tex]triangle \: abd \\ using \: pythagoras \: theorem \\ {hyp}^{2} = {adj}^{2} + {opp}^{2} \\ {12}^{2} = {3}^{2} + {opp}^{2} \\ 144 = 9 + {x}^{2} \\ 144 - 9 = {x}^{2} \\ 135 = {x}^{2} \\ take \: the \: square \: of \: both \: sides \\x = 11.62[/tex]

using the opposite side of triangle and

[tex]using \: pythagoras \: theorem \\ {16}^{2} = {11.62}^{2} + {x}^{2} \\ 256 = 135.02 + {x}^{2} \\ 256 - 135.02 = {x}^{2} \\ 120.198 = {x}^{2} \\ take \: the \: roots \: of \: both \: sides \\ x = 10.96[/tex]

therefore the length of line AC

[tex] = 3 + 10.96 \\ = 13.96[/tex]

hope this helps



HELP URGENT 30 POINTS

Answers

Answer:

              vertex

ray

Step-by-step explanation:

The point where the rays intersect, upper right, is the vertex.

One side of the angle, bottom left, is a ray.

First is line point second is endpoint

Find the indicated measures, given that EA is a diameter

a) mDEF =
b) mEFG =
c) mAC=

d) Explain how you found each angle measure below. Be sure to show all of your work.

Answers

Using the knowledge of the measure of a semicircle, the measures in the circle given are:

a. m(DEF) = 152°

b. m(EFG) = 70°

c. m(CA) = 28°

What is the Measure of a Semicircle?

Half of a circle is a semicircle = 180°.

Given the following:

m(CDE) = 152°m(FG) = 31°m(AG) = 110°m(DC) = m(EF) = 180 - 110 - 31 = 39° (semicircle)

a. m(DEF) = [m(CDE) - m(DC)] + [m(EF)]

m(DEF) = (152 - 39) + 39

m(DEF) = 152°

b. m(EFG) = m(EF) + m(FG)

m(EFG) = 39 + 31 = 70°

c. m(CA) = 180 - 152 (semicircle)

m(CA) = 28°

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find the area of a circle whose radius is 14cm​

Answers

Answer:

Formula for area of circle;

A = π[tex]r^{2}[/tex]

Where 'π' represents pi(3.14 or 22/7), and 'r' stands for the radius which is being squared.

What we know:

Radius = 14cm

Plug in what we know;

A = π[tex]r^{2}[/tex]

(For pi I'll be using 3.14 instead of 22/7)

A = 3.14(14^2) ← (The symbol ' ^ ' means to the power of.)

A = 3.14(196)

A = 615.44, 615.44 centimetres is the area of this circle.

Answer:

≈[tex]615.44cm^2[/tex]

Step-by-step explanation:

So the equation for area of circle.

[tex]\pi r^2\\\pi 14^2[/tex]

So 14^2, or 14 x 14 is 196.

Now you can either keep it in terms of pi, 196pi, or times it by pi.

[tex]196*pi\\196*3.14\\615.44[/tex]

So the answer would be around 615.44cm^2

example problems for area

Answers

Answer:

Example 1.

A square with side lengths of 5.

5*5 = 25.

So the area would be 25 units ^2

Example 2.

A rectangle with a length of 9 and a width of 4

9*4 = 36

So the area is 36 units ^2

Answer:

ans: 75

Find the area of a rectangle in square inches with a length of 15 inches and a width of 5 inches in sq. inches.

__________________________________________________________

ans: 113.10

Find the area of a circle with a diameter of 12 inches in square inches.

What is the slope of
the line?

Give your answer as
a fraction in simplest
form.

Answers

Answer:

3/4

Step-by-step explanation:

The answer is 3/4, because we rise 3 and run 4 the formula is always rise over run, and thats why its 3/4

Hoped this helped!!

There is a bag containing 7 red marbles, 2 blue marbles, 8 green marble and 12 yellow marbles. Rodolfo Ronaldo will choose 3 marbles without replacement. How many possible outcomes does this experiment have?

Answers

Answer:

22707

Step-by-step explanation:

If 8 pounds of ground beef cost $10.32, how much would 12 pounds cost?

Answers

Answer:

$15.48 for 12 lbs

Step-by-step explanation:

Check photo for work

The 12 pounds of ground beef cost is  $15.48.

What is unitary method ?

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

According to the question

8 pounds of ground beef cost $10.32

i.e  8 pounds of ground beef = $10.32

    1  pounds of ground beef = [tex]\frac{10.32}{8}[/tex]

    1  pounds of ground beef = $1.29

Therefore,

12 pounds of ground beef = 1.29*12

12 pounds of ground beef = $15.48

Hence, 12 pounds of ground beef is of  $15.48.

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please help!!!

A store is advertising a sale with 15% off all prices in the store.
Sales tax is 8%.

Which expressions represent the total cost of buying an item with an original price of p, after the discount and sales tax are included?

A. 1.08p - 0.15p
B. 1.15p + 0.08p
C. 1.08(0.85p)
D .85p + (0.08)(0.85p)
E. p - 0.15p + 0.08p

Answers

Answer:

D

Step-by-step explanation:

im too lazy to type so i write it out instead


5
The length of each small square is
½inch.
What is the area of the rectangle?
A.
5 square inch
64
B.
5
16
square inch
C.
oo square inches
D. 2, square inches

Answers

Answer:5/16 sq inch

Step-by-step explanation:

muliply heigh by width

4/8 times 5/8

a prism is completely filled with 96 cubes that have edge lengths of 1/2 cm. What is the volume of the prism?
Enter your answer in the box.​

Answers

Answer:

12 cubic cm

Step-by-step explanation:

[tex]V_{1\: cube} = \bigg( \frac{1}{2} \bigg )^{3} = \frac{1}{8} \: {cm}^{3} \\ \\ \implies \:V_{96\: cubes} = 96 \times \frac{1}{8} \: {cm}^{3} = 12\: {cm}^{3} [/tex]

It is given that: prism is completely filled with 96 cubes.

[tex]\implies \: V_{prism} =V_{96\: cubes}[/tex]

[tex]\implies \: \huge \red{V_{prism} = 12\: {cm}^{3}}[/tex]

Use substitution to solve the system.
- 3x + y = 14 and
2x + 3y = -2
x=[]
y=[]

Answers

Answer:

x=-4

y=2

Step-by-step explanation:

y= 14+3x

2x+3y =-2

2x+3(14+3x) =-2

x= -4

y= 14+3(-4)

y=2

It takes staff members 162 minutes total each night to clean all six ovens. If each staff
member works for 18 minutes, how many staff members does it take to clean the
ovens?

Answers

Answer:

9

Step-by-step explanation:

If it takes 162 minutes each night to clean all 6 ovens, and each staff member works for 18 minutes each then we have to use division to find out how many staff members it will take to clean the ovens.

First we have to divide 162 by 18 which equals 9. This is a one step problem, so 9 is the answer.

It will take 9 staff members to clean all 6 ovens.

Happy Holidays

It takes 9 staff members to clean all six ovens, with each staff member working for 18 minutes.

Given that total cleaning time is 162 minutes

Time per staff member is 18 minutes

To find the number of staff members (N), we divide the total cleaning time by the time per staff member:

N = Total cleaning time / Time per staff member

N = 162 minutes / 18 minutes

N = 9

Therefore, it takes 9 staff members to clean all six ovens, with each staff member working for 18 minutes.

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4x+4=2x-6 solve for x homework due for tomorrow

Answers

Answer:

-5

[tex] \: [/tex]

Step-by-step explanation:

[tex] \: [/tex]

Given Equation,

[tex] \\ {\longrightarrow{ \qquad{{ {\pmb{\rm { 4x+4=2x-6}}}}}}} \\ \\[/tex]

Subtracting 4 from both sides we get :

[tex] \\ {\longrightarrow{ \qquad{{ {\pmb{\rm { 4x+4 - 4=2x-6 - 4}}}}}}} \\ \\[/tex]

[tex]{\longrightarrow{ \qquad{{ {\pmb{\rm { 4x=2x-10}}}}}}} \\ \\[/tex]

Subtracting 2x from both sides we get :

[tex] \\ {\longrightarrow{ \qquad{{ {\pmb{\rm { 4x - 2x= 2x-10 - 2x}}}}}}} \\ \\[/tex]

[tex]{\longrightarrow{ \qquad{{ {\pmb{\rm { 2x= -10 }}}}}}} \\ \\[/tex]

Dividing 2 from both sides we get :

[tex] \\ {\longrightarrow{ \qquad{{ {\pmb{\rm { \frac{2x}{2} = - \frac{10}{2} }}}}}}} \\ \\[/tex]

[tex]{\longrightarrow{ \qquad{{ {\pmb{\frak { x= -5 }}}}}}} \\ \\[/tex]

Therefore,

The value of x is -5

Select the correct answer.
Solve the quadratic equation below.

Answers

Answer:

First choice

Step-by-step explanation:

X= - 2/3; - 20/9

X^2 + 18x + 81 = 25
what are the solutions

Answers

Answer:

Step-by-step explanation:

use quadratic formula answers -4,-14

What is the volume of this prism?​

Answers

Answer:

56.25    units^3

Step-by-step explanation:

To find the volume, multiply the three dimensions

3.75 * 3 * 5 =

I will mark brainlest or wtv its called

Answers

Answer:

A

Step-by-step explanation:

-7 is the farthest left on the number line so it is the least value

-5 is the second least value on the numberline

then 0

1/4

and 1/2

the least value is on the left and the greatest is on the right

so the answer is A

If the function f(x) = 5(2x) is squared, which function is produced?

Answers

The function is a linear function, and the equation of the function when squared is (f(x))² =25(4x²)

How to determine the new function?

The equation of the function is given as:

f(x) = 5(2x)

When the function is squared, we have:

(f(x))² =(5(2x))²

Evaluate the exponent

(f(x))² =25(4x²)

Hence, the equation of the function when squared is (f(x))² =25(4x²)

Read more about functions at:

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A prism is completely filled with 96 cubes that have edge length of 1 cm. What is the volume of the prism? Enter your answer in the box. . 412 cm​

Answers

Answer:

96

y-step explanation:

volume of 1cm cubes = 1 x 1 x 1 = 1 cm^3

so it will take 96 cubes to fill the prism

Amy and Julie are going camping.
Each of them both has a bag of marshmallows. The bag of marshmallows has 30 marshmallows inside. The girls also bring crackers. If Amy and Julie make 15 s'mores, how many crackers and marshmallows did they use?

Answers

Answer:

60 marshmallows and 30 crackers

Step-by-step explanation:

Each girl brought a bag of marshmallows containing 30 marshmallows inside. 2 x 30 = 60 marshmallows altogether.

Since there are 15 s'mores, we have to distribute the marshmallows equally.

60 ÷ 15 = 4 marshmallows in each. But if we multiply that again ( 15 x 4 ) we get 60 again. Thus, they used 60 marshmallows altogether.

The girls make 15 smores. A s'more has two crackers inside one.

2 x 15 = 30 crackers.

Hope this helped.

Answer:

60 marshmallows and 30 crackers

explanation:

1. 15 x 4 = 60

60 divided by 15 = 4

2. 15 x 2 = 30

What is the value of 5 in 50.14

Answers

Answer:

5 is in hundreds place, 0 is in the tens place, 1 is in the tenths place and 4 is in the hundreths place.

Step-by-step explanation:

Round -13.457 to nearest integer

Answers

Answer:

Answer:

-13

Step-by-step explanation

Rounded to the nearest 0.01 or

the Hundredths Place.

Algebra Find the value of x.

Answers

Answer:

To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.y-step explanation:

Which triangle below represents a
90° rotation about the origin?

Answers

Answer:

Because of the ratio in 2 becomes 3-1 is 2

231 - 7a = 98
How to solve this

Answers

Answer:

19

Step-by-step explanation:

231 - 7a = 98 = -7a + 231 = 98

Subtract 231 from both sides to get -7a = -133

Divide by -7 on both sides to get a = 19

Answer:

a = 19 is the correct solution.

Step-by-step explanation:

Step 1 : Start by simplifying both sides of the problem.

231 − 7a = 98

231 + − 7a = 98

−7a + 231 = 98

Step 2 : Next step is to subtract 231 from both sides

−7a + 231 − 231 = 98 − 231

−7a = −133

Step 3: Finally, divide both sides by -7.

( When I use the symbol /, it signifies I'm dividing.)

-7a/-7 = -133/-7

-133 divided by -7 equals 19

This shows that a = 19. I hope this helps! :D  

A coach brought 4 quarts of a sports drink to a game. At the end of the game, only 3 cups remained. How many cups of sports drink did the players drink during the game?

Answers

Answer:

the sports players drank 13 cups

Step-by-step explanation:

1 cup equals 0.25 quarts which means 1 quart would equal 4 cups. This means there were 16 cups in total during the game. If there were only 3 cups left afterwards, that means 13 of the 16 cups were taken.

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