Question

i need help !!!! please cos 2θ = 13 sin θ − 6 even if you just give me the answer that would be great

Answer 1

Are you trying to prove the identity, or solve for tetha?

Answer 2

solve for theta

Answer 3

Is there a domain? ex, from 0 to 2pi?

Answer 4

nope it just says solve the equation

Answer 5

Very well, This shouldn't be hard then.

Answer 6

So, start by moving everything to the left side.

You get 6+cos(2x)-13sin(x)=0 (i'll use x instead of theta to make typing easier.)

Answer 7

okay

Answer 8

now using the identity 1-sin^2(x), transform cos(2x).
You get something like 7-13sin(x)-2sin^2x=0

Answer 9

Now factor

Answer 10

Should i continue?

Answer 11

Let me know, otherwise there are many others that requested my help.

Answer 12

yes please

Answer 13

Alright, so when I factored I get:

-((7+sin(x))(2sin(x)-1)=0

Multiply both sides by -1 to eliminate the negative.

Answer 14

Now you have 2 equations
7+sinx=0 or 2sinx-1=0

Answer 15

okay so sinx = 0 a

Answer 16

so solve the first equation, sinx=-7
take the inverse sine of -7. This looks like a mess, so just see what the other equation produces.

Answer 17

(2sin(x)-1)=0
add the 1, then divide by 2

sinx=(1/2)

x=5pi/6, and x=pi/6

Answer 18

okay

Answer 19

So your two answers are posted above. Hope that helped. If still confused just ask.

Answer 20

but it would be theta = ........ and ............

Answer 21

that was the answer thank you !

Answer 22

sure thing.