SOLUTION: Find the exact value of the trigonometric function sin(u-v)given that:
sin(u)= 5/13
0 < u < pi/2
cos(v)= -3/5
pi/2 < v < pi
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Question 772225: Find the exact value of the trigonometric function sin(u-v)given that:
sin(u)= 5/13
0 < u < pi/2
cos(v)= -3/5
pi/2 < v < pi
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
is in QI, so both sin and cos are positive.
\ =\ \frac{5}{13})
\ =\ \frac{25}{169})
\ =\ \frac{25}{169})
\ =\ \frac{144}{169})
\ =\ \pm\frac{12}{13})
Discard negative because of QI.
\ =\ \frac{12}{13})
Use the same technique to find )
based on the value of )
is in QII, so \ >\ 0)
Once you have the values for the 4 functions, use those values in the formula for the sine of the difference:
\ =\ \sin\theta\cos\varphi\ -\ \cos\theta\sin\varphi)
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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