SOLUTION: If {{{sin(theta)=5/13}}} is in quadrant 2, what is the value of {{{sin((theta)+(3pi/2))}}}

Algebra ->  Trigonometry-basics -> SOLUTION: If {{{sin(theta)=5/13}}} is in quadrant 2, what is the value of {{{sin((theta)+(3pi/2))}}}      Log On


   

Question 1107873: If sin%28theta%29=5%2F13 is in quadrant 2, what is the value of sin%28%28theta%29%2B%283pi%2F2%29%29
Found 2 solutions by stanbon, ikleyn:
Answer by stanbon(75887) About Me  (Show Source):
Answer by ikleyn(52889) About Me  (Show Source):
You can put this solution on YOUR website!
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If sin%28theta%29=5%2F13 is in quadrant 2, what is the value of sin%28%28theta%29%2B%283pi%2F2%29%29
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  sin%28%28theta%29%2B%283pi%2F2%29%29 = sin%28theta%29%2Acos%283pi%2F2%29+%2B+cos%28theta%29%2Asin%283pi%2F2%29 = 

= sin%28theta%29%2A0+%2B+cos%28theta%29%2A%28-1%29 = -cos%28theta%29 = abs%28sqrt%281-sin%5E2%28theta%29%29%29 = abs%28sqrt%281-%285%2F13%29%5E2%29%29 = abs%28sqrt%281-25%2F169%29%29 = abs%28sqrt%28144%2F169%29%29 = 12%2F13.


Abs is taken,  since the angle theta is in QII, where cosine is negative; therefore, -cos%28theta%29 is positive.