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 ><

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1 Answer
Sonnhard
Jul 8, 2018

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.

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