SOLUTION: Use the characteristics of f(t) = sin t to find the value of sin t when t=-21π/4 I badly need your help :-( as I dont really know how to solve this. here are the choices to

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Question 1079851: Use the characteristics of f(t) = sin t to find the value of sin t when t=-21π/4 I badly need your help :-( as I dont really know how to solve this.
here are the choices to choose from
a. sin t = 0
b. sin t = 1
c. sin t = -√2/2
d. sin t = √2/2

Found 3 solutions by MathLover1, MathTherapy, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

f%28t%29+=+sin%28+t%29,find the value of sin+%28t%29 when t=-21pi%2F4+
f%28t%29+=+sin%28+-21pi%2F4%29=1%2Fsqrt%282%29=sqrt%282%29%2F2
answer:
d. sin+%28t%29+=+sqrt%282%29%2F2

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Use the characteristics of f(t) = sin t to find the value of sin t when t=-21π/4 I badly need your help :-( as I dont really know how to solve this.
here are the choices to choose from
a. sin t = 0
b. sin t = 1
c. sin t = -√2/2
d. sin t = √2/2
21pi%2F4 is in the 3rd quadrant, but -+21pi%2F4 is in the 2nd quadrant, and has a REFERENCE angle of matrix%281%2C3%2C+3pi%2F4%2C+or%2C+135%5Eo%29. 
Thus,

Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
The angle %28-21pi%29%2F4 is geometrically equivalent to %28-21pi%29%2F4+%2B+2pi = %28-21pi+%2B+8pi%29%2F4 = -13pi%2F4,


which, in turn, is geometrically equivalent to

-13pi%2F4%2B2pi = %28-13pi%2B8pi%29%2F4 = -5pi%2F4,


which, in turn, is simply the same as 3pi%2F4.


The function sine is periodical with the period of 2pi, therefore,


sin%28%28-21pi%29%2F4%29%29 = sin%28%28-13pi%29%2F4%29 = sin%28%28-5pi%29%2F4%29%29 = sin%283pi%2F4%29 = sqrt%282%29%2F2.

Solved.