## anonymous 5 years ago Use identities (no calculators) to nd the exact value for (sin pi/4)(cos pi/2) + (cos pi/4)(sin pi/2)

1. anonymous

this ones the hardest of them all

2. anonymous

but if you have a look at it, see what expansion it looks like

3. anonymous

and it becomes pretty easy

4. anonymous

this = sin(pi/4 + pi)??

5. anonymous

no

6. anonymous

sorry pi/2 + pi/4

7. anonymous

=sin 3/4 pi = sin 75 degrees

8. anonymous

i/m lost now!!

9. anonymous

can sin 75 degrees be written in surd form?

10. anonymous

its not 75 :|

11. anonymous

but sin75 can be written in surd form

12. anonymous

no hold om 3/4 pi = 3/4 X 180 = 135 degrees ruyght?

13. anonymous

in which case sin 135 = 1 /sqrt 2

14. anonymous

you can use sum angles expansion to find exact value of sin75 sin75 = sin(30+45) = sin30cos45+cos30sin45

15. anonymous

yes

16. anonymous

my brains not working to well today !

17. anonymous

Mathematica returns zero after entering the problem expression. The left side of the + sign is zero because Sin[Pi]= zero. Same way for the right side.

18. watchmath

It is equal to $$\sin(\frac{\pi}{4}+\frac{\pi}{2})=\sin(3\pi/4)=\sqrt{2}/2$$

19. anonymous

(Sin pi/4) was processed as Sin(pi)/4 by Mathematica.

20. anonymous

Wolfram may be incorrect but they are reporting that $\text{Sin}\left[\frac{3 \pi }{4}\right]=\frac{1}{\sqrt{2}}$