Please show steps Find the exact value of cossin1 13Solutio

Please show steps!

Find the exact value of cos[sin^-1 (- 1/3)]

Solution

Solution:

To work out the general formula for cos(arcsin(x)). Here we go;

Let = arcsin(x) => sin = x

cos(arcsin(x)) will become: cos

Also, you should note that arcsin(x) will return the values in the interval [-/2, /2]

i.e. is in I and IV quadrant, and its cosine value should be positive. so we have;

cos = (1 - sin²) = (1 - x²)

Applying the formulla in the question;

cos[sin^-1 (-1/3)] = (1 - (-1/3)²) = (1 - 1/9) = 22 / 3