Question

Consider this equation. cos ⁡ ( θ ) = 4 ⁢ 41 41 if θ is an angle in quadrant iv, what is the value of sin ⁡ ( θ ) ? a. - 5 ⁢ 41 41 b. 5 4 c. 5 ⁢ 41 41 d.

Answer 1

To find the value of sin(θ) given cos(θ) = 4/41 in quadrant IV, use the Pythagorean identity sin²(θ) + cos²(θ) = 1 and solve for sin(θ). The value of sin(θ) is approximately sqrt(1665)/41.

Step-by-step explanation:

To find the value of sin(θ) given cos(θ) = 4/41 in quadrant IV, we can use the Pythagorean identity: sin²(θ) + cos²(θ) = 1. Since we know cos(θ) = 4/41, we can solve for sin(θ) as follows:

sin²(θ) + (4/41)² = 1

sin²(θ) + 16/1681 = 1

sin²(θ) = 1 - 16/1681 = 1665/1681

sin(θ) = sqrt(1665/1681)

sin(θ) ≈ sqrt(1665)/41

Therefore, the value of sin(θ) is approximately sqrt(1665)/41.