Question

Double Angle formula

Answer 1

I only need help finding cos(x) and tan(x). I used the formula but I guess I am solving the wrong way.

Answer 2

@Mertsj

Answer 3

The problem says to find cos(2x) not cos x

Answer 4

i did this \[2(\frac{ 5\sqrt{61} }{ 61 })^{2} -1\]

Answer 5

i used the the double angle formula for cos

Answer 6

\[\cos (2x)=2\cos ^2x-1=2(\frac{5}{\sqrt{61}})-1=\frac{10\sqrt{61}}{61}-1\]

Answer 7

so you're not supposed to do the exponent first?

Answer 8

where is the squared?

Answer 9

\[\tan 2x=\frac{2\tan x}{1-\tan ^2x}=\frac{2(\frac{6}{5})}{1-(\frac{6}{5})^2}=\frac{\frac{12}{5}}{1-\frac{36}{25}}\]

Answer 10

\[\frac{\frac{12}{5}}{\frac{-11}{25}}=\frac{12}{5}\times\frac{-25}{11}=\frac{-60}{11}\]

Answer 11

Oh gees...I have to do the cosine one again. I did forget to square it. Maybe I'll use the other identity.

Answer 12

actually can you do that one..because the square tricks me and I think that is why i did it wrong

Answer 13

\[\cos 2x=\cos ^2x-\sin ^2x=(\frac{5}{\sqrt{61}})^2-(\frac{6}{\sqrt{61}})^2=\frac{25}{61}-\frac{36}{61}=\frac{-11}{61}\]

Answer 14

would it be positive because it is in QUAD 1?

Answer 15

i got that answer but i put pos bc it is in quad 1

Answer 16

If x is in quadrant 1, 2x could be in quadrant 2, if the angle is more than 45

Answer 17

ohhh got it..thanks for explaining and taking the time to help me. I appreciate it!

Answer 18

And if the tangent is 6/5, the angle if 50 degrees so 2x is in quadrant 2 and the cos and tan would be negative.

Answer 19

yw