Posted by **jared** on Monday, November 7, 2011 at 12:37am.

given that sin(a+b)= 56/65, cos(a+b)-33/65, cos(b)=-12/13 and pi/2<b<pi

Find:

sin(a)?

cos(a)?

tan(a)?

- trig -
**Steve**, Monday, November 7, 2011 at 5:59pm
Assuming that cos(a+b) = -33/65

sin(a+b) = sin a cos b + cos a sin b

cos(a+b) = cos a cos b - sin a sin b

-12/13 sin a + 5/13 cos a = 56/65

5/13 sin a + 12/13 cos a = -33/65

Multiply by 5 to clear denominators:

-60 sin a + 25 cos a = 56

25 sin a + 60 cos a = -33

sin a = -507/845

cos a = 676/845

so,

tan a = -507/676

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