Question

Given sin(θ) = 24/31 in Quadrant I, evaluate cos(θ):

a) Positive value
b) Negative value
c) Reciprocal value
d) Zero value

Answer 1

In Quadrant I, if sine is positive, then cosine is positive.

Step-by-step explanation:

In Quadrant I, the sine function is positive and the cosine function is positive.

Given that sin(θ) = 24/31, we can use the Pythagorean identity to find cos(θ). Using the equation sin^2(θ) + cos^2(θ) = 1, we have (24/31)^2 + cos^2(θ) = 1.

Solving for cos(θ), we find cos(θ) = ±√(1 - (24/31)^2), which simplifies to cos(θ) = ±7/31.