Question

Let θ be an angle in the first quadrant, and suppose sin(θ)=a. Evaluate the following expressions in terms of a:

(a) cos(θ)
(b) tan(θ)
(c) csc(θ)
(d) sec(θ)
(e) cot(θ)

Answer 1

To evaluate the expressions, use the trigonometric identities for sine and cosine. For example, cos(θ) can be evaluated as √(1 - sin²(θ)).

Step-by-step explanation:

To evaluate these expressions in terms of a:

(a) cos(θ) = √(1 - sin²(θ)) = √(1 - a²)

(b) tan(θ) = sin(θ)/cos(θ) = a/√(1 - a²)

(c) csc(θ) = 1/sin(θ) = 1/a

(d) sec(θ) = 1/cos(θ) = 1/√(1 - a²)

(e) cot(θ) = 1/tan(θ) = √(1 - a²)/a