Posted by Sierra on Wednesday, November 7, 2012 at 10:51am.
How do you find the exact value of sin 5pi/8?

trig  Steve, Wednesday, November 7, 2012 at 11:08am
cos2θ = 1  2sin^2 θ
since 2θ = 5pi/4, cos 2θ = 1/√2
1/√2 = 1  2sin^2 5π/8
2sin^2 5π/8 = 1 + 1/√2
sin 5π/8 = √(1 + 1/√2)/2
= √(2+√2) / 2

trig  Damon, Wednesday, November 7, 2012 at 11:17am
You are talking about 112.5 degrees
that is 90 + 22.5
22.5 is half of 45
so draw this in the third quadrant
I know functions of 45 degrees
sin 45 = +1/sqrt 2
cos 45 = +1/sqrt 2
so what are the functions of 22.5 degrees?
sin(45/2) = +/ sqrt[(1cos 45)/2]
cos (45/2) = +/sqrt[(1+cos 45)/2]
in this case we want the negative cos for the sin (look at sketch) because in quadrant 3
so sin 112.5 = sqrt [ (1+1/sqrt 2)/2]
= sqrt [ (1 + sqrt 2)/2 sqrt 2
= sqrt [ (2+sqrt2)/4 ]
=  .923
check sin 112.5 on calculator = .923

trig  note  Steve, Wednesday, November 7, 2012 at 11:22am
sin is positive in QII

trig  Damon, Wednesday, November 7, 2012 at 2:52pm
whoops, sorry
Answer This Question
Related Questions
 trig  find the exact value by using the appropriate halfangle identity: sin(...
 trig  using the fact that 5pi/8=1/2(5pi/8) and the half angle identity for cos ...
 Trig functions  1)Write the equation sin y= x in the form of an inverse ...
 Math/Precal  How do i find the exact value for (Cos 5pi/16)(Cos pi/16) + (sin ...
 Trig hep, please? Thank you!  1. Find the exact value of sin(195(degrees)) 2. ...
 Trig  Find the exact value of tan 5pi/12 using the halfangle identity.
 trig  Find the exact value of the trigonometic function at the given real ...
 math  use exact values of the sin,cos and tan of (pi/3) and (pi/6)(which I ...
 trig/pre calc  hello, i don't quite understand how to do this type of problem...
 Trig  Given: sin x = 4/5, 0 < x < ?/2 sin y = 5/13, ?/2 < y < ? ...
More Related Questions