Question 925555: How do I evaluate these this two sine and cosine problems. Difficult!?
Evaluate cos(a − b) if cos a = 4/5 tan a < 0, tan b = −√15 and cos b < 0
cos(a-b) =
and
Evaluate sin(x + y) if sin x = 3/5 sec x > 0, cos y = − (2√5)/5 and tan y < 0.
sin(x + y) =
THANKS!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! evaluate these this two sine and cosine problems. Difficult!?
Evaluate::
cos(a − b) if cos a = 4/5 tan a < 0,
Note:: a is in QII where x is positive and y is negative
Since cos = x/r, x = 4 and y = -sqrt(5^2-4^2) = -3
Then sin(a) = y/r = -3/4
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tan b = −√15 and cos b < 0
Note:: b is in QII where x is negative and y is positive
Since tan = y/x, y = sqrt(15) and x = -1
Then sin(b) = y/r = sqrt(15)/sqrt((sqrt(15))^2+1^2) = sqrt(15)/4
and cos(b) = x/r = -1/4
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cos(a-b) = cos(a)cos(b)+sin(a)sin(b)
----
= (4/5)*(-1/4) + (-3/4)(sqrt(15)/4)
=====================================
and
Evaluate sin(x + y) if sin x = 3/5 sec x > 0, cos y = − (2√5)/5 and tan y < 0.
sin(x + y) =
---Whoops:: Got to run. Maybe you can finish this now.
Cheers,
Stan H.
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