SOLUTION: Use the cofunction theorem to fill in the blank so the expression becomes a true statement. a) sin pi/6 =cos________ B) cot 1= tan___________ c) cos90 degrees =sin_____

Algebra ->  Trigonometry-basics -> SOLUTION: Use the cofunction theorem to fill in the blank so the expression becomes a true statement. a) sin pi/6 =cos________ B) cot 1= tan___________ c) cos90 degrees =sin_____      Log On


   

Question 544936: Use the cofunction theorem to fill in the blank so the expression becomes a true statement.
a) sin pi/6 =cos________ B) cot 1= tan____________
c) cos90 degrees =sin_____________ D) csc (80 degrees -x)=sec_____________
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If the cofunction of an angle is the function of its complement, all you have to do in each case is find the angle that woould add to 90 degrees or pi%2F2 radians.
a) for pi%2F6 the angle you are looking for is pi%2F2-pi%2F6=pi%2F3, so
sin%28pi%2F6%29=cos%28pi%2F3%29
Those are angles you should be familiar with pi%2F6=30degrees, pi%2F3=60degrees, and sin%2830degrees%29=cos%2860degrees%29
b) cot(1 radian)? or is it cot(1 degree)?
cot%281+degree%29=tan%2889degrees%29
if in radians, cot%281%29=tan%28pi%2F2-1%29
c) cos(90 degrees)=sin(0 degrees)
d) 90 degrees - (80 degrees -x)= 90 degrees - 80 degrees +x=10 degrees +x
csc (80 degrees -x)=sec (10 degrees +x)