Question

Jse the function values and the trigonometric identities to evaluate each trigonometric function. sec(θ)=9,tan(θ)=45

(a) cos(θ)
(b) cot(θ)
(c) cot(90°−θ)
(d) sin(θ)

Answer 1

To evaluate trigonometric functions, we can use the given values of sec(θ) and tan(θ) and apply the relevant trigonometric identities. Using these identities, we find the values of cos(θ), cot(θ), cot(90°−θ), and sin(θ).

Step-by-step explanation:

To evaluate the given trigonometric functions, we can use the given values of sec(θ) and tan(θ) and apply the relevant trigonometric identities. Let's go through each function:

(a) To find cos(θ), we can use the identity cos(θ) = 1/sec(θ). Since sec(θ) = 9, cos(θ) = 1/9.

(b) To find cot(θ), we can use the identity cot(θ) = 1/tan(θ). Since tan(θ) = 45, cot(θ) = 1/45.

(c) To find cot(90°−θ), we can use the identity cot(90°−θ) = tan(θ). Since tan(θ) = 45, cot(90°−θ) = 45.

(d) To find sin(θ), we can use the identity sin²(θ) = 1 − cos²(θ). We know that cos(θ) = 1/9, so sin²(θ) = 1 − (1/9)² = 1 − 1/81. Taking the positive square root, sin(θ) = √(1 − 1/81).