Answer:
1) θ = 130°
2) θ = 310°
Step-by-step explanation:
We want to find a value of θ such that:
sin(θ) = sin(50°)
We know that sin(90°) = 1
We will have a symmetry around 90°.
Then if we define a constant k
sin(90° + k) = sin(90° - k)
we can define k such that:
90° - k = 50°
90° - 50° = k
40° = k
Then:
sin(90° + 40°) = sin(90° - 40°)
sin(130°) = sin(50°)
then θ = 130°
Now we want to find:
cos(θ) = cos(50°)
We know that cos(0°) = 1
Then we have symmetry around 0°
With the same reasoning than before, we can write:
cos( 0° + k) = cos(0° - k)
We can define:
0° + k = 50°
k = 50°
Then:
cos(50°) = cos(-50°)
But we want 0° < θ < 360°
Knowing that the peridisity of the trigonometric functions is of 360° then:
cos(50°) = cos(-50°) = cos( - 50° + 360°)
cos(50°) = cos(310°)
in this case θ = 310°
