The value of Θ

[SamanthaMFR]

The equation Sin(Θ-10°)=k, 0≤Θ=360° has a solution Θ=40° for a given value of k.
For the given value of k, the other solution is Θ =
a) 20°
b) 50°
c) 140°
d) 160°

How can I answer this question? I dont know where to start to solve it.

 

[daon2]

The equation Sin(Θ-10°)=k, 0≤Θ=360° has a solution Θ=40° for a given value of k.
For the given value of k, the other solution is Θ =
a) 20°
b) 50°
c) 140°
d) 160°

How can I answer this question? I dont know where to start to solve it.

First find the value of k by substituting the given theta.

 

[Ishuda]

The equation Sin(Θ-10°)=k, 0≤Θ=360° has a solution Θ=40° for a given value of k.
For the given value of k, the other solution is Θ =
a) 20°
b) 50°
c) 140°
d) 160°

How can I answer this question? I dont know where to start to solve it.

Another possible way to solve it if you know the sine of sum and difference of angles formulas: What is the sin(\(\displaystyle \pi-\phi)\)? Then let \(\displaystyle \phi = \theta - 10^{\circ}\).

 

[SamanthaMFR]

So k would be equal to sin(30)= 1?

 

[ksdhart]

k is equal to sin(30°), yes. But sin(30°) does not equal 1. And since you know k (well, once you fix the minor error), you can then find the other value of theta that satisfies the equation.