You need to learn some trigonometric identities:
1. sin(A+B) = sin(A)cos(B)+cos(A)sin(B)
2. sin(A-B) = sin(A)cos(B)-cos(A)sin(B)
3. cos(A+B) = cos(A)cos(B)-sin(A)sin(B)
4. cos(A-B) = cos(A)cos(B)+sin(A)sin(B)
5.
5.
6.
7.
8.
9. for all integers n
10. for even integers n
for odd integers n
Suppose csc t = 4 and tan t > 0
4 is positive so csc is positive and tangent is positive,
so t is in quadrant 1.
The cosecant is , so draw a right
triangle containing angle t. Make the hypotenuse 4 and the
side opposite angle t be 1. Then csc(t) will be 4/1 or 4.
Since the hypotenuse = 4 and the opposite side = 1, then
So we put on the adjacent side:
sin(t - 6π) =
First use 2 above.
Now use 9 and 10 above
cot(5π-t) =
First use 7 above
Now use 4 and 2
Now use 9 and 10 and the right triangle to substitute for all the sines
and cosines
cos(-t) =
Write -t as 0-t and use 4
Now use 9 and 10 and the right triangle to substitute for all the sines
and cosines
sin(2t) =
Write 2t as t+t and use 1:
Use the right triangle above to substitute for the sines and cosines:
cos(t+5π/3) =
Use 8
Use 3
300° is one of the special angles in quadrant IV with reference angle 60°
,
Edwin