Please help with these trig problems

find the Quadrant and Value
a) cos480 degrees
b) sin15pi/4
c) tan(-10pi/4)
d) cot630 degrees

a)

cos(480)

= cos( 360 + 120)

= cos(120)

= cos(180 - 60)

= - cos(60)

= - 1/2 (II quadrant)

b)

sin(15π/4)

= sin(4π - π/4)

= -π/4 (IV quadrant)

= -√2/2

c)

tan(-10π/4)

= - tan(10π/4)

= - tan(2π + π/2)

= - tan(π/2) (II quadrant)

= undefined

d)

cot(630)

= cot(720 - 90)

= -cot(90) (IV quadrant)

= 0

just a reminder: those angles on the axes are not in quadrants

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First find the coterminal angle between 0 and 360 by adding or subtracting n*360.

( in radians, add or subtract n*2 pi)

A) cos 480 = cos 120. This is a 60 degree angle in quadrant II. cos 120= -1/2

B) sin 15pi/4

15 pi/4 - 8 pi/4 = 7 pi/4 which is a 45 degree angle in quadrant IV.

Sin (7pi/4) = -(sqr2)/2

C) tan (-10 pi/4)

-10pi/4= -5pi/2

-5pi/2 + 4pi/2+ 4pi/2= 3pi/2, on the axis between Quad III and IV

tan(3pi/2) = sin(3pi/2) / cos(3pi/2) which is -1/0 , undefined.

D) cot 630
630-360= 270, on the axis, between Quad. III and IV

Cot (270) = cos(270)/ sin(270) = 0/-1= 0

Hoping this helps!

cos480=cos120 = -1/2 , 2nd quadrant