Trig, i think???

Question

hi there, i have know idea were to start in this question,

find the general solution of the equation
cos4& = cos3&

& = theta

do you have to use one of the trig identities?

thanks alot for your help!!

Answer 1

Expand cos 4x according to the identities and do the same for cos3x. then substitute cos3x for y or something and solve as a normal quadratic eqn

Answer 2

You are looking for some angles when two cosines are the same. The simplest thing to do is to simply compare the angles themselves.

The first is pretty simple. In order for the cosines to be equal then the angles must be equal. So:
4T = 3T and T = 0

Also the case where the angles are in different quadrants. First quad cosines equal fourth quad cosines (or second and third, the result is the same). So:
4T = 360 - 3T or 3T = 360 - 4T
7T = 360 and T = 51.4286 degrees

If that 4T = 360 - 3T is not clear, think about an angle A in the first quad and what angle gives the same cos in the fourth quad. It is just 360 - A.

Check that last answer:
4T = 205.71423 and cos = -.90097
3T = 154.28571 and cos = -.90097

Answer 3

cos4 θ= cos3θ then either 4θ=3θ then θ=0

or 4 θ = 360 - 3θ

then θ =360/7 =51˚ 25' 43''

Answer 4

Use Cos (A+B) = CosA* CosB + SinA * SinB

For Cos(4 theta) = Cos (2theta + 2theta)
then Cos(2theta) = Cos(theta + theta)
Similarly, Cos(3 theta) = Cos(2 theta + heta)..................
..........................Cos(2 theta) can then be again resolved.

None of the big trig identities. Only Cos(A+B) addition

Answer 5

I gotta D in trig.