Question

0° ≤ n ≤ 90°

Solve the following equations when 90° ≤ x ≤ 360°,
giving your answers in terms of angle n:
a) sin x = sin n
b) cos x = cos n
c) tan x = tan n

Answer 1

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.