Solve the following, where 0° < 𝜃 < 360°, If 5/2 cos 𝜃 + 4 = 2, find 𝜃.

Question

Really bad at trig, any help would be nice :)

Answer 1

 5/2 cos 𝜃 + 4 = 2, find 𝜃.

5/2 * cos θ =-2

cos θ =-8

θ=143.1301..........

Answer 2

5/2cosx+4=2

5/2Cosx=-2

5cosx=-4

cosx=-4/5 Take inverse cosine of both sides to solve for x

x=-143.1degrees and -143.1degrees

Answer 3

Sam, please note that the question states clearly that the answer must lie between 0⁰ and 360^o

Therefore, negative angles or angles ≥ 360^o are excluded from the solution set.

5/2 cosΘ + 4 = 2

5/2 cosΘ = -2

cosΘ = -4/5

Now cos is -ve in in Q2 and Q3

and cosΘ = +4/5 => Θ = 36^o 87' . . . . . . . from a scientific calculator (or Google!)

So, our required values of Θ are 180^o - 36^o 87' and 180⁰ + 36^o 87'

= 143^o 13' and 216^o 87'

Solution set: {143^o 13' ; 216^o 87'}