Final answer:
To solve these equations involving trigonometric functions, we use the properties of periodicity.
For a) and b), the solutions are x = n + 360°, and for c), there is no solution.
Step-by-step explanation:
a) sin x = sin n
Since the sine function is periodic with a period of 360°, we can write x = n + 360°k, where k is an integer.
Since we are given that 90° ≤ x ≤ 360°, we know that k must be greater than or equal to 1.
Therefore, the solution is x = n + 360°.
b) cos x = cos n
Similar to part a, the cosine function is also periodic with a period of 360°.
So x = n + 360°k. However, since we are given that 90° ≤ x ≤ 360°, we know that k must be greater than or equal to 1.
Therefore, the solution is x = n + 360°.
c) tan x = tan n
For the tangent function, since it is periodic with a period of 180°, we can write x = n + 180°k, where k is an integer.
However, since we are given that 90° ≤ x ≤ 360°, we know that k must be greater than 1.
Therefore, there is no solution for this equation.