SOLUTION: Rewrite the expression as the​ sine, cosine, or tangent of a​ double-angle. Then find the exact value of the trigonometric expression without the use of a calculator.

Algebra ->  Trigonometry-basics -> SOLUTION: Rewrite the expression as the​ sine, cosine, or tangent of a​ double-angle. Then find the exact value of the trigonometric expression without the use of a calculator.       Log On


   

Question 1100862: Rewrite the expression as the​ sine, cosine, or tangent of a​ double-angle. Then find the exact value of the trigonometric expression without the use of a calculator.
2cos^2 (-30°)-1
a. Use the appropriate​ double-angle formula to rewrite the given expression as the​ sine, cosine, or tangent of the corresponding​ double-angle.
​(Do not evaluate. Type your answer in degrees.)
b.Find the exact value of the trigonometric expression without the use of a calculator.
​(Use integers or fractions for any numbers in the expression. Type an exact​ answer, using radicals as​ needed.)

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


(a) 2%28cosx%29%5E2-1 is a double angle formula for cosine; so
2%28cos%28-30%29%29%5E2-1+=+cos%28-60%29

(b) -60 degrees is a reference angle of 60 degrees in quadrant IV; cosine is the x value on the unit circle; that is the short leg of a 30-60-90 right triangle; its length is 1/2.

Answer: 2%28cos%28-30%29%29%5E2-1+=+cos%28-60%29+=+1%2F2