Fundamentals of University Mathematics, 3rd Edition

Appendix D

Properties of Trigonometric Functions

Throughout, θ and ϕ are real numbers.

1. – l ≤ sin θ ≤ l,   –1 ≤ cos θ ≤ 1.

2. sin² θ + cos² θ = 1,   tan² θ + 1 = sec² θ,  1 + cot² θ = cosec² θ.

3. For k ∈ ,  sin(θ + 2kπ) = sin θ  (period 2π),

      cos(θ + 2kπ) = cos θ  (period 2π),

      tan(θ + kπ) = tan θ  (period π).

4. sin(–θ) = –sin θ  (odd function),

    cos(–θ) = cos θ  (even function),

    tan(–θ) = –tan θ  (odd function).

5. sin ( ± θ) = cos θ,  cos ( ± θ) =  sin θ.

6. The diagram shows in which quadrants lie the angles for which sin, ...