Question

For an angle with measure x in a right triangle, sin x = 112/113

and tan x = 112/15. What is the value of cos x?

Answer 1

To find the value of cos x, use the Pythagorean identity and the given information to calculate cos x.

Step-by-step explanation:

To find the value of cos x, we can use the Pythagorean identity.

Since sin x = 112/113, we can let the opposite side be 112 and the hypotenuse be 113. Using the identity, cos^2 x = 1 - sin^2 x, we can calculate cos x as follows:

cos^2 x = 1 - (112/113)^2

cos^2 x = (113^2 - 112^2) / 113^2

cos^2 x = (12769 - 12544) / 12769

cos^2 x = 225 / 12769

cos x = √(225 / 12769)