How do you find the exact value of sin(3pi/8) using the DOUBLE ANGLE FORMULAS?

Question

Please tell specifically WHAT you do and HOW...
because i have to do many more questions just like this one!
THANK YOU!

Answer 1

cos(2A) = 1 - 2 (sinA)^2

Let A = 3pi/8. Then 2A = 6pi/8 or 3pi/4

cos(3pi/4) is known to be -sqrt(2)/2

So - sqrt(2) / 2 = 1 - 2 (sinA)^2

2 (sinA)^2 = 1 + sqrt(2)/2

(sinA)^2 = (1 + sqrt(2)/2)/2

sq rt of both sides gives the exact value of sin 3pi/8.

Hope that helps!

Answer 2

I don't know how you do it with double-angle formulas, but you can do it with half-angle formulas.

sin(3π/8) = sin[(1/2)*(3π/4) = √[1 - cos(3π/4)]/2

cos(3*π/4)= cos[(1/2)*(3π/2)] = -√[1+cos(3π/2]/2

cos(3π/2) = 0, so cos(3π/4) = -√(1/2)

which makes sin(3π/8) = √[(1 + √.5)/2] which can be rationalized to (1/2)*√[2+√2]