Trigonometric Equations

Precalculus Quiz

 







Trigonometric equation can be solved by using standard algebraic techniques such as collecting like terms and factoring. The initial goal in solving a trigonometric equation is to isolate the trigonometric function in the equation.

Example:




Because cos(x) has a period of 2π, first find all solutions in the interval [0, 2π).
The solutions are π/4 and 7π/4.

The general solution of the equation can be found by adding multiples of 2π to each of these solutions: π/4 + 2nπ and 7π/4 + 2nπ.



Solve the following equations:



1:

, 0 ≤ x < 2¶












2:

, 0 ≤ x < 2¶











3:

, 0 ≤ x < 2¶












4:

, 0 ≤ x < 2¶












5:

, 0 ≤ x < 2¶

















6:

, 0 ≤ x < 2¶











7:

, 0 ≤ x < 2¶











8:

, 0 ≤ x < 2¶













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