Standard position and reference angles

Question

Given angles O= -9pie/4 and B=510 degrees, draw them in standard position and find their reference angles, O and B. Use the reference angle to find the exact values of sin (-9pie/4) and tan 510 degrees 

Answer 1

O= -9pi/4 is in quadrant IV where sines are negative

reference angle = -9pi/4 +8pi/4+ pi/2 = pi/2-pi/4 = pi/4 = 45 degrees

sin45 = exactly sqr2/2 = about 0.707

but sin(-9pi/4) = sin(-pi/4)

= sin(-45)= -sqr2/2 = about -0.707

P = 510 degrees is in quadrant II where tangents<0

reference angle =510-360-90= 150 -90= 60 degrees=pi/3

tan60 = sqr3/1 = sqr3

but tan510 = sqr3/-1 = -sqr3