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
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.