Question

What is cos(2a) equal to if cos(a) = 0.3?

Answer 1

\[\cos(2a)=\cos^2(a)-\sin^2(a)\]
use this formula and
\[\sin^2 a+\cos^2 a=1\]

Answer 2

If cos a = .3, a = 72.5 degrees and 2a =145 degrees. The cosine of 145 degrees is -.82

Answer 3

how do we get 72.5

Answer 4

Enter .3 into your calculator and push second function cosine.

Answer 5

i dont see a function key on my calc

Answer 6

Do you have a cosine button?

Answer 7

yea

Answer 8

What does it say right above the cosine button?

Answer 9

you should click on \(cos^{-1}\) button

Answer 10

cos^-1

Answer 11

Bingo!!!

Answer 12

and to do that you need go to 2nd floor

Answer 13

kool do you know how to do this also

Answer 14

there's button called 2nd

Answer 15

yeah i know how to do that now...i was just wondering if you knew how to also do this question
Give an algebraic expression for cos(sin^−1(x)). Here sin^−1(x) stands for the compositional inverse of sin(x).

Answer 16

sin^-1(x) means "an angle whose sin is x" So if we call that angle y, for instance then we are talking about cos(y)

Answer 17

ok

Answer 18

Or, if we are talking about the unit circle:

Answer 19

Then x^2+y^2 = 1 and y = (1-x^2)^1/2 so the sin of the angle is x and the cosine is y or sqrt(1-x^2)