Mathematics College

find csc θ and sec θ if cot θ= 3/2 and cos θ>0​

Find Csc And Sec If Cot = 3/2 And Cos >0

Answers

Answer 1

Since both cot(θ) and cos(θ) are positive, it follows that sin(θ) is also positive:

cot(θ) = cos(θ)/sin(θ) > 0   ===>   sin(θ) > 0

Recall the Pythagorean identity:

sin²(θ) + cos²(θ) = 1

Multiplying both sides by 1/sin²(θ) yields another form of the identity,

sin²(θ)/sin²(θ) + cos²(θ)/sin²(θ) = 1/sin²(θ)

1 + cot²(θ) = csc²(θ)

so that

csc(θ) = + √(1 + cot²(θ))

csc(θ) = √(1 + (3/2)²)

csc(θ) = √13/2

By definition of cosecant, we have

csc(θ) = 1/sin(θ)

so that

sin(θ) = 2/√13

Then using the Pythagorean identity once more, we have

cos(θ) = + √(1 - sin²(θ))

cos(θ) = √(1 - (2/√13)²)

cos(θ) = 3/√13

so that, by definition of secant,

sec(θ) = 1/cos(θ)

sec(θ) = √13/3

Related Questions

is y=3 and x=5 perpendicular?

Answers

Answer:

yes

Step-by-step explanation:

One is a horizontal line, and the other is a vertical line.

Answer: Yes, if you graph the two lines, they have the negative recipricol of the other answer.

Step-by-step explanation:

which data set shows greater variability ?why?
A or B

shows greater variability because the MAD is greater that the MAD for
A or B​

Answers

My guess is A because the data shows greater variability

Solve for x
X-11=-2

Help

Answers

Answer:

9

Step-by-step explanation:

x - 11 = - 2

x = - 2 + 11

= 11 - 2

x = 9

◻︎                                                                                                                            ◻︎

                                            Hello There!

We must make sure numbers are on the right side of the equation and x's (variables) are on the left:

x=-2+11

x=9

Hope this helps you! :)

Answered by:

[tex]GraceRosalia[/tex]

HELP US PLS I WILL GIVE BRAINLIEST!!!!!

Answers

this is what I think
Is the question asking what you should if so the answer is unit rate because a unit rate means a rate of one to something while a rate is a ratio which the two terms are in different units. Since it is divided the most it can it is a unit rate

PLEASE HELP WILL MARK BRAINIEST!! TY!!

Answers

[tex]y = -3x + 27[/tex]

Step-by-step explanation:

A parallel line will have the same slope as the given line so we can write the slope-intercept form of the equation as

[tex]y = -3x + b[/tex]

Since the other line goes through the point (9, 0), we can use this to solve for b:

[tex]0 = -3(9) + b \Rightarrow b = 27[/tex]

Therefore, the equation of the parallel line that goes through (9, 0) is

[tex]y = -3x + 27[/tex]

At the beginning of the season, MacDonald had to remove 5 orange trees from his farm. Each of the remaining trees produced 210 oranges for a total harvest of 41790 oranges.
Write an equation to determine the initial number of orange trees (t)(t)left parenthesis, t, right parenthesis on MacDonald's farm.

Answers

Answer: t = (total harvest/ harvest per tree) + number of trees removed

Step-by-step explanation:

total harvest/ harvest per tree will give the number of trees on the farm.

translate this into an equation, use n for the number: "the different of 3 times a number and 6 is twice the number."

Answers

Answer:

6

Step-by-step explanation:

6 * 3 = 18

18 - 6 = 12

12 is twice of 6, the number

What’s the new function of g(x)

Answers

Answer:

The answer is the first one. It's also in my picture that I included

The length of a rectangular sign is 5 times its width. If the sign’s perimeter is 24 inches, what is the sign’s area?

Answers

Answer:

A=20

Step-by-step explanation:

Let the width be x

x=width. 5x =L

2(L+W)=p

2(5x+x) =24

10x+2x=24

12x=24

12x/12 =24/22

x=2

A =LxW

A = (5x2)x x

A =10 x2

A=20

Simplify, then solve

Answers

Answer:

Where is equation to solve??

WHAT IS 300% ON 100 ?

Answers

Answer:

300.

Step-by-step explanation:

that's the answer.

Answer:

The answer would be 300

Step-by-step explanation:

300 x 100 = 30000

30000 ÷ 100 = 300

Hope this helps!!

To complete a job, a plumber needs 10 sections of pipe that are 24.125 inches in length. How much pipe is needed?

Answers

Answer:

241.25

Step-by-step explanation:

24.125 x 10= 241.25

Answer:

That would be a total of 241 and a quarter inches of pipe which is equal to 20.10417 feet of pipe.

Step-by-step explanation:

24.125x10=241.25/12=20.104166666

Because there are 12 inches in a foot.

—
what's .612 with twelve repeating as a fraction in its simplest form?

Answers

Answer:

101/165

Step-by-step explanation:

Answer:

101/165

Step-by-step explanation:

5.8x+13.9=3.1x-15.8 solve for X

Answers

Answer:

-11

i hope that helps!

5.8x+13.9=3.1x-15.8

X=-11

please help :(. i don’t know how to do this

Answers

Hey you can get this app that read the maths questions and gives u the answer straight away so u don’t need to wait for people to answer you

b. One room is 8 ft wide and 12 ft long.
Another room is 9 ft wide and 15 ft
long. What is the difference in area?

Answers

Answer:

12-8

15-9

Step-by-step explanation:

The perimeter P of a triangle is equal to the sum of the lengths of sides a, b, and c.

Answers

The given statement "The perimeter P of a triangle is equal to the sum of the lengths of sides a, b, and c" is absolutely correct.

What is the perimeter?

Perimeter is the addition of an external measure of sides it will always positive.

A perimeter is a length and has a degree of the unit as one.

For example

Perimeter of square = side + side + side + side

The perimeter of the circle = πd where d is the dia of the circle.

Given a triangle with sides a,b and c

The perimeter of triangle is = a + b+ c

So,

The perimeter of the triangle is the sum of all sides.

Hence The given statement "The perimeter P of a triangle is equal to the sum of the lengths of sides a, b, and c" is absolutely correct.

To learn more about Perimeter,

https://brainly.com/question/6465134

#SPJ2

Use the drop-down menus to complete the statements below to compare the values of the two expressions. 2 attachments

Answers

The value of the expression in blue is 18 times the value of the expression in red

I know this because the sum of y and z is multiplied by 18

Answer:

The value of the expression in blue is 18 times the value of the expression in red

I know this because the sum of y and z is multiplied by 18

10% of what is 80,000?

Answers

Answer:

let the no be x ..then,

10% of x =80,000

10x=80,000*100

x=80,00,000/10

x=8,00,000

hence 10%of 8,00,000 is 80,000

At the movie theatre, child admission is $5.20 and adult admission is $8.40. On Wednesday, 154 tickets were sold for a total sales of $1069.60. How many adult tickets were sold that day?

Answers

Answer:

127

Step-by-step explanation:

1069.60 divided by 8.40 equals 127.

Find the equation of the line. A line that is perpendicular to the graph of 3x +2y =6 and contains the point (6,-3)

Answers

9514 1404 393

Answer:

  2x -3y = 21

Step-by-step explanation:

The perpendicular line will have an equation with the x- and y-coefficients swapped and one of them negated. The constant will be the value that makes the equation true at the given point.

  3x +2y = 6 . . . . . given equation

  2x -3y = c . . . . . . coefficients swapped, one negated

  2(6) -3(-3) = c = 21 . . . . . the value of c for the given point

The desired equation is ...

  2x -3y = 21

I need help with this please​

Answers

Answer:

23 26 25

24 21 27

29 22 28

Step-by-step explanation:

23+25= 48

74-48= 26

This way find all the values.

can someone explain how to solve the angle A

Answers

I cannot explain but from various examples that I have seen I would say that Angle A is either 30°, 40°, or 45°

HELPPPPP AGAIN!!! THIS IS DIFFICULT

Answers

To find the perimeter you must
11-7=4
That’s the?answer

An angle measures 64.8° more than the measure of its supplementary angle. What is the measure of each angle?

Answers

Answer: angle 1 = 56  and angle 2 = 124

Step-by-step explanation:

Supplementary angle equal 180 degrees

   let X be angle 1 and X +68 be angle 2

    x + x + 68 = 180

     2x + 68 = 180

          - 68     - 68

      2x = 112

        x = 56

        x + 68 = 56 + 68 = 124

An online school with 125 classes has a student enrollment of 2,500 students. Which rate represents the relationship between the student enrollment and the number of classes? 12 classes per student 20 classes per student 20 students per class 30 students per class

Answers

Answer 20 classes per student

Step-by-step explanation:

(I need help)
Compute each of the following mentally.
a.) 160 + 92 – 32 + 40 – 18


b.) 36 + 97 – 80 + 44

Answers

Answer:

b. 9

Step-by-step explanation:

36+97=133

80+44=124

133-124=9

please help me
23 y (2 + 4) =

Answers

Answer:

[tex]23y(2 + 4) = 23y(6) = 138y[/tex]

Ben gets $50 per day as wages and $6.00 as commission for every book he sells in a day. His daily earnings goal is $140.
Using the equation constructed in previous question, solve for the
number of books he must sell to meet his daily earnings goal.


Answers

$140 = $6 per book • x books + $50

Subtract $50 from $140 and you get:
$90 = $6 per book • x books

Divide $90 by $6 per book:
And you get x = 15 books

Answer:

the basic wage is 50$

the extra to get 140$ is 90$(140-50)

.............

as for 1 book he get 6$

so for ? book he get 90$

then ? =(90$*1)/6$= 15 book

that's it hope i helped.

PLEASE HELP ME AND HURRY TOO NO LIBKS PLEASE I WILL GIVE BRAINLIEST

Answers

Answer:

[tex] \frac{1}{3} x - 5 - \frac{1}{6} x - 3 = \\ \frac{2}{6} x - \frac{1}{6} x - 8 = \frac{1}{6} x - 8[/tex]

Answer:

option D is the right answer

please mark this answer as brainlist

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