# trig

posted by .

Find the exact value by using a half-angle identity. cos 22.5 degrees

• trig -

use
cos 2A = cos^2A - sin^2A
cos2A = cos^2A - (1 - cos^2A) = 2cos^2A - 1
cos 45° = 2cos^2 22.5° - 1
√2/2 + 1 = 2cos^2 22.5
√2/4 + 1/2 = cos^2 22.5°
cos 22.5° = √[ (√2 + 2)/4 ]
= √(√2 + 2) /2

## Similar Questions

1. ### Algebra II

1) Find the exact value of cos 105 degrees by using a half-angle formula. 2)Find the solution of sin 2theta = cos theta if 0 degrees</= theta < 180 degrees. I have read the book and looked at the examples, but cannot figure out …
2. ### MATH

1.)Find the exact solution algebriacally, if possible: (PLEASE SHOW ALL STEPS) sin 2x - sin x = 0 2.) GIVEN: sin u = 3/5, 0 < u < ï/2 Find the exact values of: sin 2u, cos 2u and tan 2u using the double-angle formulas. 3.)Use …
3. ### trig

using the fact that 5pi/8=1/2(5pi/8) and the half angle identity for cos to find the exact (in terms of radicals) value of cos(5pi/8)
4. ### trig

find the exact value by using the appropriate half-angle identity: sin(5pi/12)
5. ### Trigonometry

use the appropriate trig identity (sum and difference, half angle, double angle) to find the exact value. 1)cos 255 degrees 2) sin 165 degrees 3) tan 285 degrees
6. ### Algebra II

Multiple Choice (theta) means the symbol 0 with the dash in it. 1.)Which expression is equivalent to tan(theta)-(sec(theta))/(sin(theta))?
7. ### Trig

Find the exact value of tan 5pi/12 using the half-angle identity.
8. ### TRIG/ALGEBRA

1) Find the exact value. Use a sum or difference identity. tan (-15 degrees) 2) Rewrite the following expression as a trigonometric function of a single angle measure. cos 3x cos 4x - sin 3x sine 4x
9. ### Trig

Use a half-angle identity to find the exact value for sec(x/2) if sinx = -12/13 ; 3pi/2 < x < 2pi
10. ### trig

use a half-angle identity to find the exact value of tan 105 degrees.

More Similar Questions