Question
use a half angle formula to find the exact value of cos 75 degree
Answers
Reiny
start with
cos 2A = 2cos^2 A - 1
cos150° = 2 cos^2 75 - 1
-√3/2 + 1 = 2cos^2 75°
cos^2 75° = (1 - √3/2)/2
cos 75° = √[(1 - √3/2)/2]
An easier ways would have been
cos75 = cos(45+30)
= cos45cos30 - sin45sin30
= (1/√2)(√3/2) - (1/√2)(1/2)
= (√3 - 1)/(2√2)
Use your calculator to show that both produce cos75
cos 2A = 2cos^2 A - 1
cos150° = 2 cos^2 75 - 1
-√3/2 + 1 = 2cos^2 75°
cos^2 75° = (1 - √3/2)/2
cos 75° = √[(1 - √3/2)/2]
An easier ways would have been
cos75 = cos(45+30)
= cos45cos30 - sin45sin30
= (1/√2)(√3/2) - (1/√2)(1/2)
= (√3 - 1)/(2√2)
Use your calculator to show that both produce cos75