Finding General Solutions of Trigonometric Equations

The general solution of a trigonometric equation is a formula that provides all possible angles (solutions) that satisfy the equation, typically expressed in terms of a variable (k) representing any integer.

$$x = \frac{2\text{π}}{3} + 2k\text{π} \text{ or } x = \frac{4\text{π}}{3} + 2k\text{π}, k \text{ in } \text{ℤ}$$ .

$$x = \frac{(2k+1)\text{π}}{4}, k \text{ in } \text{ℤ}$$ .

$$x = \frac{\text{π}}{3} + k\text{π}, k \text{ in } \text{ℤ}$$ .

$$x = \frac{k\text{π}}{3}, k \text{ in } \text{ℤ}$$ .

$$x = \frac{\text{π}}{3} + 2k\text{π} \text{ or } x = \frac{2\text{π}}{3} + 2k\text{π}, k \text{ in } \text{ℤ}$$ .

The range of the sine function is from -1 to 1, inclusive.

The range of the cosine function is from -1 to 1, inclusive.

The period of the sine function is $$2\text{π}$$ .

The period of the cosine function is $$2\text{π}$$ .