Question

If sin x= 7/8 , x in quadrant I, then find:

a) cos x= −√15/8
b) cos x= √15/8
c) cos x= √15/7
d) cos x= −√15/7

Answer 1

The value of cos x when sin x = 7/8 in quadrant I is sqrt(15)/8.

Step-by-step explanation:

To find the value of cos x when sin x = 7/8 in quadrant I, we can use the Pythagorean identity: sin^2(x) + cos^2(x) = 1. Substitute sin x = 7/8 into this equation: (7/8)^2 + cos^2(x) = 1. Solve for cos x: cos^2(x) = 1 - (7/8)^2 = 1 - 49/64 = 15/64. Taking the square root of both sides, we get: cos(x) = +sqrt(15)/8 or -sqrt(15)/8. Since x is in quadrant I, where cosine is positive, the correct answer is cos x = +sqrt(15)/8.