SOLUTION: Pleas help me solve this equation: find sin(s-t) given that cos s=1/3, with s in quadrant I, and sin t=-1/2, with t in quadrant IV
Algebra ->
Trigonometry-basics
-> SOLUTION: Pleas help me solve this equation: find sin(s-t) given that cos s=1/3, with s in quadrant I, and sin t=-1/2, with t in quadrant IV
Log On
Question 865803: Pleas help me solve this equation: find sin(s-t) given that cos s=1/3, with s in quadrant I, and sin t=-1/2, with t in quadrant IV Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! solve this equation: find sin(s-t) given that cos s=1/3, with s in quadrant I, and sin t=-1/2, with t in quadrant IV.
***
cos s=1/3
sin s=√(1-cos^2 s)=√(1-1/9)=√(8/9)=√8/3
sin t=-1/2
cos t=√(1-sin^2 s)=√(1-1/4)=√(3/4)=√3/2
Identity: sin(s-t)=sin s*cos t-cos s*sin t=√8/3*√3/2-1/3*-1/2=√24/6+1/6=(√24+1)/6
sin(s-t)=(√14+1)/6
..
calculator check:
cos s=1/3
s≈70.5288˚
sin t=-1/2
t=330˚
s-t≈-259.47˚
sin(s-t)=sin(-259.47)≈0.9831
exact value=(√24+1)/6≈0.9831
(