Question

If θ is an acute angle in the first quadrant such that sin⁡θ=5/13​, which one of the following is true?

A. cos⁡(90∘−θ)
B. sin⁡(90∘−θ)
C. tan⁡(90∘−θ)
D. tan⁡(90∘−2/5)=−1/2

Answer 1

To determine which one of the given options is true, we can find the value of cos(90° - θ) by using the complementary angle identity cos(90° - θ) = sinθ. Since sinθ = 5/13, we can conclude that cos(90° - θ) = 5/13.

Step-by-step explanation:

To determine which one of the given options is true, we need to find the value of cos(90° - θ). Since sinθ = 5/13, we can use the Pythagorean identity sin²θ + cos²θ = 1 to find the value of cosθ. First, we can find sin²θ by squaring the value of sinθ: sin²θ = (5/13)² = 25/169. Next, we can substitute sin²θ into the Pythagorean identity: cos²θ = 1 - sin²θ = 1 - 25/169 = 144/169. Finally, we can find cosθ by taking the square root of cos²θ: cosθ = √(144/169) = 12/13.

Now, we can find the value of cos(90° - θ) by using the complementary angle identity cos(90° - θ) = sinθ. Since sinθ = 5/13, we can conclude that cos(90° - θ) = 5/13.