Elementary trig equations and general solutions

Elementary trigonometric equations and general solutions

Practise solving equations involving sine, cosine and tangent on a specified interval or across all real angles. This precalculus set distinguishes a principal inverse-trigonometric value from a complete solution set. Exact angles, symbolic inverse values and both radian and degree intervals help you build solutions systematically instead of reporting only the calculator’s first answer.

The questions progress from unit-circle recognition to integer-parameter families, interval filtering, endpoint decisions and impossible equations. Single-select and multiselect tasks ask for all valid solutions where appropriate. Detailed explanations show how the function’s sign and symmetry identify the branches, how its period repeats them, and why the original interval must be checked at the end.

Preparation and checking

Review principal inverse-function ranges, exact unit-circle values and interval notation. State whether angles are in radians or degrees, and treat the integer parameter as any integer when describing an all-real family. Substitute proposed angles back into the original equation. This set focuses on elementary unscaled angles; factoring and affine angle expressions are developed in the following practice sets.