# Maths

Prove that sine inverse x = cosec inverse 1/x

1. 👍
2. 👎
3. 👁
1. Draw the unit circle.
Draw a right triangle in standard position (right angle on the x-axis).

Now label the sides.
The hypotenuse is 1
The height is x
Let angle A be at (0,0)

So, sin(A) = x/1 = x
That is, A = sin^-1(x)

csc(A) = 1/sin(A) = 1/x
So, A = csc^-1(1/x)

1. 👍
2. 👎

## Similar Questions

1. ### inverse

If f(x)=cosx + 3 how do I find f inverse(1)? Thanks y = cos(x) + 3 the inverse of this is x = cos(y) + 3 solve for y and you have your inverse The cos function only has a range of [-1,1], so the range of f(x) is [2,4]. this means

2. ### Linear Algebra

which of the following functions is the inverse of F(X)=3x F(X)=-3X F(X)=X (cubed)**** F(X)= X/3 This function does not have an inverse. Thank you!

3. ### Algebra

Is the relationship between the variables inthe table a direct variation, an inverse variation, both, or neither? If it is a direct or inverse variation write a function to model it x: 2, 5, 12, 20 y: 30, 12, 5, 3 A. Direct

Did I get these practice questions right? 1. Suppose that f is an even function whose domain is the set of all real numbers. Then which of the following can we claim to be true? ***The function f has an inverse f –1 that is

1. ### Trig/Math

To find an angle where you have the opposite and adjacent which formula do you use? Sine, Cosine, Tan? and how do you find the inverse?

2. ### College Algebra

Find the inverse of the function below. Graph the function below and the inverse function. Determine the domain, range, and asymptotes of the function below and the inverse function. Please show all of your work. Show both graphs.

3. ### Algebra 2

formula for converting celcius to fahrenheit: F=9/5C+32 a) what is the inverse of the function? b)use the inverse to find the celcius tempertature that corresponds to 25F Please help i have no idea how to solve this :(

4. ### Precalculus

Find the inverse of g(x)=(1/3x)-7 and then find its domain and range. I already found the inverse of the function.

1. ### Pre-Cal: Word Problem

I'm having a lot of trouble on this word problem. Can someone help me plz? To define the inverse sine function, we restrict the domain of sine to the interval ______. On this interval the sine function is one-to-one, and its

2. ### Algebra

Myra uses an inverse variation function to model the data for the ordered pairs below. (2, 30), (3, 20), (4, 15), (5, 12), (6, 10) Which statement best explains whether an inverse variation function is the best model for the data?

3. ### Algebra

I have to find the inverse function of f(x)=3-4x. I got y=3-x/4 for the function. I then have to plug it back into the function and verify that it is the inverse. So I wrote (3-4(3-x))/4. This resulted in (-3+x)/4=x. I tried

4. ### Trigonometry

Having trouble with true/false questions in Trigonometry. They read as follows - True or False: For a trigonometric function, y=f(x), then x=F^-1(y). Explain your answer. True or False: For a one to one function, y=f(x), then