Exact Value of Quadrantal Angle - Trig

Question

If there are not any write undefined. Is there an equation without using the calculator? I have access to the Trigonometric Function Values of Quadrantal Angles.

1. tan (4π) I got 0 from looking at the chart but not sure how to justify.
2. csc 5π/2
3. sin (-2π) also got 0 from the frequently used angle circle, then the chart because -2π same as 360degrees
4. cos (-3π/2)

Answer 1

tan(4pi)= tan2pi =tan0 = 0

= opposite side over adjacent side = o/a = 0/1 = 0

csc(5pi/2)= 1/sin(5pi/2)=1/sin(pi/2)= 1/1/1= 1

sin-2pi= sin0 = 0

cos(-13i/2)= cos(pi/2)= 0/1= 0

Answer 2

Answer 3

tan(4π) = tan(4π - 2π) = tan(2π) = sin(2π) / cos(2π) = 0/1 = 0

csc(5π/2) = csc(5π/2 - 2π) = csc(π/2) = 1 / sin(π/2) = 1/1 = 1

sin(-2π) = -sin(2π) = -0 = 0 (in general, sin(-θ) = -sinθ)

cos(-3π/2) = cos(-3π/2 + 2π) = cos(π/2) = 0