Question

cos theta = 4/5, 0˚< theta < 90˚ use the information given to find sin2theta, cos2theta, and tan 2theta

Answer 1

you need \(\sin(\theta)\) so compute these
do you know how to find it?

Answer 2

the identities?

Answer 3

sin 2 theta = 2 sin theta cos theta
cos 2 theta = 2 cos ^2 theta - 1
tan 2 theta = sin 2 theta / cos 2 theta

Answer 4

do i plug in 4/5 where theta is?

Answer 5

If costheta=4/5 then sintheta= 3/5
\[\sin2\theta=2\sin\theta \cos\theta\]

Answer 6

there is a picture of an angle whose cosine is \(\frac{4}{5}\) you find the third side by pythagoras, or recalling the 3 - 4 - 5 right triangle
this tells you \(\sin(\theta)=\frac{3}{5}\)

Answer 7

oh okay

Answer 8

so 2 sin theta = 2 sin 3/5 cos 4/5

Answer 9

no do not make that mistake, it is a common one
do not use \(\theta=\frac{4}{5}\) use \(\cos(\theta)=\frac{4}{5}\) so \[\sin(2\theta)=2\times \frac{4}{5}\times \frac{3}{5}\]

Answer 10

no not the cosine and sine of those numbers, those numbers ARE the cosine and sine

Answer 11

use the numbers themselves, they are your sines and cosines

Answer 12

okay thank you!

Answer 13

your good now right?

Answer 14

im still confused a little ..