Asked by Katie
How do you find cos15
Answers
Answered by
Reiny
from the 30-60-90 triangle you should know that cos 30º = √3/2
from the identity
cos 2A = 2cos^2 A - 1
cos 30 = 2cos^2 15 - 1
√3/2 + 1 = 2cos^2 15
cos15 = √[(√3/2 + 1)/2]
or an easier way
cos15
= cos(45-30)
= cos45cos30 + sin45sin30
= (√2/2)√3/2) + (√2/2)(1/2)
= (√6 + √2)/4
which yields the same result as avove, check with calculator
from the identity
cos 2A = 2cos^2 A - 1
cos 30 = 2cos^2 15 - 1
√3/2 + 1 = 2cos^2 15
cos15 = √[(√3/2 + 1)/2]
or an easier way
cos15
= cos(45-30)
= cos45cos30 + sin45sin30
= (√2/2)√3/2) + (√2/2)(1/2)
= (√6 + √2)/4
which yields the same result as avove, check with calculator