Question

Medals and fan for days!

Given that cos(2theta)=3/8, with 2theta terminating in Q4.

a) Theta terminates in what quadrant?
(just divide by 2?)

b) Use an appropriate double angle formula to compute an exact value for cos(theta).

Answer 1

\[\cos(2 \theta)=\frac{3}{8}\]

\[\cos(2 \theta)=\cos^2(\theta)-\sin^2(\theta)=1-2 \sin^2(\theta)\]
cos(2theta) is given
replace cos(2 theta) above with 3/8 and solve the equation for sin(theta)

Answer 2

or better yet since you want cos(theta)
look at \[\cos(2 \theta)=\cos^2(\theta)-(1-\cos^2(\theta))=2 \cos^2(\theta)-1 \]
\[\cos(2 \theta)=2 \cos^2(\theta)-1 \]
this instead

Answer 3

this bottom equation replace the cos(2 theta) with 3/8 and solve for cos(theta)

Answer 4

also if you want to find theta
you know 2theta is between 270 and 360
so solve this inequality for theta 270<2 theta <360

Answer 5

now when you solve that one equation for cos
you will have two values to choose from
use the fact where theta is and what sign cos should be there to pick out which sign you need

Answer 6

awesome, thanks so much!

Answer 7

do you want me to check your answers?

Answer 8

believe it's in Q2 so would be neg

Answer 9

yeah give me one second to compute it

Answer 10

omg you are so great
that is so right
so far

Answer 11

-(squareroot11)/4?

Answer 12

that is absolutely right

Answer 13

thanks for the help magical unicorn!

Answer 14

np lol