How can the solutions to a trig equation be determined?

[MMCS]

Hi,

I have the answers to the following question, but i do not know how to calculate them from the first:

Find all the solutions to the following equation

Sin( (5x)/2 + 15°) = 0.34

Where 0°≤x≥360°

The answers are (1.950749625,58.04925038,145.9507496,202.0492504,289.9507496,346.0492504)

My attempt

sin^-1(0.34)=19.88

19.88-15 = 4.88

(4.88*2)/5 = 1.95

How are the other answer worked out from here?

Thanks

 

[SammyS]

Hi,

I have the answers to the following question, but i do not know how to calculate them from the first:

Find all the solutions to the following equation

Sin( (5x)/2 + 15°) = 0.34

Where 0°≤x≥360°  ⟵  This should be 0° ≤ x ≤ 360° .

The answers are (1.950749625,58.04925038,145.9507496,202.0492504,289.9507496,346.0492504)

My attempt

sin^-1(0.34)=19.88

19.88-15 = 4.88

(4.88*2)/5 = 1.95

How are the other answer worked out from here?

Thanks

The general solution to $\displaystyle \ \sin(\theta)=u\$ is $\displaystyle \ \theta=\sin^{-1}(u)+(360^\circ) k\,,\ 180^\circ-\sin^{-1}(u)+(360^\circ) k\,,$ where k is an integer.

 

[HallsofIvy]

Do you know what the graph of y= sin(x) looks like? It is positive for $0\le x\le 180$ and negative for $180\le x\le 360$. And, between 0 and 180, the graph is symmetric: $sin(180- x)= sin(x)$.