Question

find the reference angle of -20000 and express the six trigonometric functions of -20000 in terms of the six trigonometric functions of its reference angle.

Answer 1

-20000/360 = -55.555555..
= -55 - 200/360

so we have 55 clockwise rotations and then another clockwise rotation of 160°
OR
360-200 = 160° in the counterclockwise of positive rotation direction

160° is in the second quadrant, where the sine is positve and we are 20° from the x-axis

so the reference angle is 20°


sin(-20000) = sin20
cos(-20000) = -cos20
tan(-20000( = -tan(20)
I will let you do the cosecant, secant, and cotangents

test the above 3 with your calculator.

that is,
sin -20000 - sin 20 should be zero, it is on mine.