Question

Use identities (no calculators) to nd the exact value for (sin pi/4)(cos pi/2) + (cos pi/4)(sin pi/2)

Answer 1

this ones the hardest of them all

Answer 2

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

Answer 3

and it becomes pretty easy

Answer 4

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

Answer 5

no

Answer 6

sorry pi/2 + pi/4

Answer 7

=sin 3/4 pi = sin 75 degrees

Answer 8

i/m lost now!!

Answer 9

can sin 75 degrees be written in surd form?

Answer 10

its not 75 :|

Answer 11

but sin75 can be written in surd form

Answer 12

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

Answer 13

in which case sin 135 = 1 /sqrt 2

Answer 14

you can use sum angles expansion to find exact value of sin75

sin75 = sin(30+45) = sin30cos45+cos30sin45

Answer 15

yes

Answer 16

my brains not working to well today !

Answer 17

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.

Answer 18

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

Answer 19

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

Answer 20

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