Question 913780: Evaluate the trig function: (Please show the step-by-step process for evaluating these two trig functions.)
sin t = 4/5
a.) sin (pi - t)
b.) sin (t + pi)
cos t =4/5
a.) cos (pi - t)
b.) cos (t + pi)
Note: We have only begun learning about the unit circle, so please don't provide an advance explanation. Thank you.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Evaluate the trig function: (Please show the step-by-step process for evaluating these two trig functions.)
sin t = 4/5 (working with a (3-4-5) reference right triangle)
a.) sin (pi - t)(starting from 0,rotate cc 180˚then back of t deg which gives you a reference angle=t in quadrant II in which sin>0. So, sin(pi-t)=sin t=4/5
b.) sin (t + pi)=sin(pi+t)(starting from 0,rotate cc 180˚then add t deg which gives you a reference angle=t in quadrant III in which sin<0. So, sin(t+pi)=sin t=-4/5
..
cos t =4/5 (working with a (3-4-5) reference right triangle)
a.) cos (pi - t)(starting from 0,rotate cc 180˚then back of t deg which gives you a reference angle=t in quadrant II in which cos<0. So, cos(pi-t)=cos t=-3/5
b.) cos (t + pi)=cos (pi+t)(starting from 0,rotate cc 180˚then add t deg which gives you a reference angle=t in quadrant III in which cos<0. So, cos(t+pi)=cos t=-3/5
note:
0pposite side of reference right triangle=4
Adjacent side of reference right triangle=3
Hypotenuse=5
sin=4/5
cos=3/5
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