Question

How to solve this trig q? Help pls?

In part a) I got 0.317. Could someone pls tell me how to get 1.36?
In part b) I got all the solutions except 221.4. Could someone pls tell me how to make the cast diagram to get that? From my second cast diag I got 138.6, 41.4 and 318.6 ><

Answer 1

For (i) we get

`theta_1=1/3arctan(7/5)` or `theta=1/3*(pi+arctan(7/5))`
For (ii) we get

`theta_=2pi-arccos(1/3)`

`theta_2=arccos(1/3)`

`theta_3=2pi-arccos(-3/4)`

`theta_4=arccos(-3/4)`

Explanation:

Writing your equation in the following form
`5sin(3theta)=7cos(3theta)`
dividing by `cos(theta)`

(note that `tan(x)=sin(x)/cos(x)`)

we get

`tan(3theta)=7/5`

solving this we get

`theta=1/3arctan(7/5)`

or

`theta=1/3(pi+arctan(7/5))`

Solution for (ii)

we have

`9cos^2(theta)+5cos(theta)-3sin^2(theta)=0`

substituting

`sin^2(theta)=1-cos^2(theta)`
and we get

`12cos^2(theta)+5cos(theta)-3=0`

substituting `t=cos(theta)`

we have to solve

`12t^2+5t-3=0`

solving this by the quadratic formula we get

`t_1=1/3`

`t_2=-3/4`
By backsubstitution we get the solutions above.