inverses of cosine functions?

Question

need help with this problem:
what is the inverse of y= (pie)/2 + cos-1x

cos-1 also means arccos

thanks :)

Answer 1

To find inverses, switch y and x, then solve for y:

x = pi/2 + cos^-1(y)

x - pi/2 = cos^-1 y

cos(x-pi/2) = cos (cos^-1)y = y

so the inverse is y = cos (x-pi/2) which is - sin x
so y = -sin x

Answer 2

Rearrange:

y - pi/2 = cos^(-1) x

Take cos of both sides:

cos(y-pi/2) = x

Use identity cos(A-B) = cos A cos B + sin A sin B:

cos y cos pi/2 + sin y sin pi/2 = x

Use cos pi/2 = 0 and sin pi/2 = 1:

x = sin y

Answer 3

I found a link that will take you to a math site that easily explains how to play with inverse trig functions.

Go to: http://www.analyzemath.com/Trigonometry.html

If, after going to the site you are still not sure of what to do, write back.

Guido

Answer 4

Ok, let's see

y = 90 deg + (cos(x))^-1

y is an angle measurement

if I understand your question correctly,

1/y = y^-1 = 1/(pi/2 + (cos(x))^-1)

good luck.

Answer 5

PIE/2 +COS-1X =SIN-1 X