Hey everyone, I couldn't figure out how how to find the value for:
I know the answer, but, I'm looking for the solution, and why.
Thanks
Hi you'll need your trigo circle to get this one.
If you look at the circle you'll notice that
$\displaystyle Sin(\frac{\pi}{2}-x)=cos(x)$
There is also a proof if you use the fact
$\displaystyle sin(a-b)=cos(b)sin(a)-cos(a)sin(b)$.
Try it now, let me know if you can't make it!
Hello, Imonars!
$\displaystyle \text{Simplify: }\:1 + \sin^2(7^o) + \sin^2(83^o)$
$\displaystyle \text{Note that: }\:\sin(83^o) \;=\;\sin(90-7) \;=\;\sin(90^o)\cos)7^o - \cos(90^o)\sin(7^o)$
. . . . . . . . . . . . . . . $\displaystyle =\;1\!\cdot\!\cos(7^o) - 0\!\cdot\!\sin(7^o) \;=\;\cos(7^o)$
$\displaystyle \text{The expression becomes: }\:1 + \underbrace{\sin^2(7^o) + \cos^2(7^o)}_{\text{This is 1}} \;=\; 2$