How do you solve #sin(pi/5-pi/2)#?
2 Answers
Explanation:
Expand use Difference of Angles.
Remember
So we can simplify it more:
That's
Explanation:
Finally a triangle that's not 30/60/90 or 45/45/90. Thank you.
This is our first tiptoe outside the two tired triangles of trig. We can find a nice radical expression for this one, which is related to the pentagon. It's a bit involved, but not too bad.
Let's do it in degrees, which always makes more sense to me.
Strap in, this is where it gets interesting. First we note
In other words, all the multiples of
Our unknown now is
It's a cubic, but an easy one because we know
The quadratic has roots
Clearly
That's
Now that wasn't too bad venturing beyond our two tired triangles of trig, was it?