find the fundamental solutions to the following equation; -18cos(theta)-15tan(theta)=-20sec(theta)

Question

give your answer in degrees.

0<(theta)<360 degrees

Find four solutions

Answer 1

dont want much du yu????????

-18 kosine(x) -15 tan(x) +20sekant(x)=0

sekant=1/kosine & tan=sine/kosine

so multipli bi kosine...-18 kosine^2 -15 sine(x) +20=0

or +18 kosine^2 +15sine -20=0

bi tri & tri agin, me get 1 anser...25.5287 deg

Answer 2

Let Theta=A. The given equation can be written: -18cosA-15tanA=-20secA ··· Eq.1

tanA=sinA/cosA and secA=1/cosA   So that, Eq.1 can be rewritten as follows:

-18cosA-15sinA/cosA=-20/cosA   Multiply both sides by cosA.

-18cos²A-15sinA=-20 ··· Eq.2  Use the identity: cos²A=1-sin²A, and plug this into Eq.2.

-18(1-sin²A)-15sinA=-20   We have:18sin²A-15sinA+2=0 ··· Eq.3  

Let sinA=t   Eq.3 can be rerwitten as follows:

18t²-15t+2=0   Factor the equation.

(6t-1)(3t-2)=0   We have: t=1/6, or 2/3    

That is: sinA=1/6, or 2/3 (0<a<360°)   So, A=arc sin(1/6), or arc sin(2/3) 

And sinA=sin(180-A)   So, (180-A)is the answer as well.

 Therefore the answer is: Theta=approx 9.594°, 41.810°, 170.406°, or 138.190°