anonymous
  • anonymous
cos theta = 4/5, 0˚< theta < 90˚ use the information given to find sin2theta, cos2theta, and tan 2theta
Trigonometry
schrodinger
  • schrodinger
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anonymous
  • anonymous
you need \(\sin(\theta)\) so compute these do you know how to find it?
anonymous
  • anonymous
the identities?
anonymous
  • anonymous
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anonymous
  • anonymous
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
anonymous
  • anonymous
do i plug in 4/5 where theta is?
anonymous
  • anonymous
If costheta=4/5 then sintheta= 3/5 \[\sin2\theta=2\sin\theta \cos\theta\]
anonymous
  • anonymous
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 \(\sin(\theta)=\frac{3}{5}\)
anonymous
  • anonymous
oh okay
anonymous
  • anonymous
so 2 sin theta = 2 sin 3/5 cos 4/5
anonymous
  • anonymous
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 \[\sin(2\theta)=2\times \frac{4}{5}\times \frac{3}{5}\]
anonymous
  • anonymous
no not the cosine and sine of those numbers, those numbers ARE the cosine and sine
anonymous
  • anonymous
use the numbers themselves, they are your sines and cosines
anonymous
  • anonymous
okay thank you!
anonymous
  • anonymous
your good now right?
anonymous
  • anonymous
im still confused a little ..

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