I need help solving these trig functions

Question

For each of these trig functions how will you go about finding the co-terminal/reference angle, exact value and graphing it in an x-y plane.

tan (-210)

sin(13pi/3)

sec (5pi/4)

Answer 1

Co terminal just means between 0 and 360 degrees. So

1. tan (-210) = tan (150), which makes a 30 degree triangle with the 180 degree line (2nd quadrant). Using the special triangle (30-60-90), you know tan = 1/√3 = √3/3, but in quadrant 2, tan is negative, so answer is -√3/3
2. sin (13π/3) = so you go around the circle 2 times, with π/3 more (1st quadrant). You know π/3 is also 60 degrees, which is the same special triangle as in #1. So the answer is √3/2
3. sec (5π/4), this is the reciprocal of cosine and is in the 3rd quadrant, so it will be negative. It is π/4 beyond 180 degrees, which is 45 degrees beyond, so 225 degrees, use special triangle 45-45-90, so cosine is 1/√2 = √2/2 for cosine, but this is for secant, so the answer is the reciprocal just at √2!