Question

if cos x = 4over11, whats cos 2A

Answer 1

\[\cos(x)=\frac{4}{11}\]
\[\cos(2x) = ?\]

Answer 2

8/22 ?

Answer 3

no, that's just multiplying the numerator and denominator by 2.

Answer 4

You would have to solve the angle which, when put into the cos function, gives you a value of 4/11

Answer 5

i dont know how to do that

Answer 6

One approach would be to use the Cosine Double angle formula.

\[\cos 2x = \cos^2 x - \sin^2 x\]

We already know the value of cos x, so we can throw that into the square thing... For sine we'll have to set up a triangle.

Answer 7

Or we could use the other cosine double angle formula actually :D that's probably easier.

\[\cos 2x=2\cos^2 x -1\]

Answer 8

\[2\left(\frac{ 4 }{ 11 }\right)^2-1\]

Answer 9

You can do this through inverse trig functions which can be thought of as the 'reverse' of trig functions:
\[\cos(x) =(\frac{4}{11})\]
\[\cancel{\cos^{-1}\cos}(x) = \cos^{-1}(\frac{4}{11})\]

Answer 10

\[x = \cos^{-1}(\frac{4}{11})\]

Answer 11

Yah if you are allowed to use a calculator, then math's method is much better :D

Answer 12

@zepdrix thanks tips

Answer 13

wait so i just slove the equation

Answer 14

im still lost

Answer 15

The question can read:
Some angle, when placed into the cosine function will give you a value of 4/11. What value do you get if you put twice that angle into the cos function.

1. first you must solve the angle, through inverse trig functions.
2. then you would multiply that angle by 2 and place it back into the cos function

Answer 16

i dont know how to do that though

Answer 17

how do i solve for an angle