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## anonymous 5 years ago Use identities (no calculators) to find the exact value for (sin 9)(sin 36)-(cos 9)(cos 36)

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1. anonymous

9+36 =?

2. anonymous

how can you play with those angles to get an angle for which there is an exact value

3. anonymous

does this equals cos 45?

4. anonymous

yes

5. anonymous

which is 1/ sqrt(2)

6. anonymous

$\sin \theta = \cos 90 - \theta$

7. anonymous

How do I figure out if its positive of negative

8. anonymous

sines, cosines and tangents in the first quadrant (0-90 degrees) are all positive

9. anonymous

i've just checked my maths formula book and the given expression = -cos(9 + 36) not cos (9+36) so the correct answer is -(1/sqrt2)

10. anonymous

this is not the formula for $cos(a+b)$ but it is its negative.

11. anonymous

of course 9+36=36+9=45

12. anonymous

but the formula for $cos(a+b)=cos(a)cos(b)-sin(a)sin(b)$

13. anonymous

and $sin(a)sin(b)-cos(a)cos(b)=-(cos(a)cos(b)-sin(a)sin(b)$ that is why you had to change the sign from $\frac{\sqrt{2}}{2}$to $-\frac{\sqrt{2}}{2}$

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