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Pre-Calculus 12
Trigonometry
5. Solve algebraically and graphically first and second-degree trigonometric equations
5.1 Solving first degree trigonometric equations
Solving First-Degree Trigonometric Equations
Isolate the trig ratio, find the reference angle, then use the quadrants where that ratio has the right sign.
What You'll Learn
A first-degree trig equation has the trig function to the first power only.
Step 1: isolate the trig function using algebra.
Step 2: find the reference angle from the isolated value.
Step 3: use the quadrants where that ratio has the correct sign.
Step 4: list every solution within the given interval.
What You'll Practice
1
Finding all solutions within 0° to 360° (or 0 to 2π radians)
2
Writing general solutions using multiples of period
3
Solving equations with sine, cosine, tangent, and reciprocal functions
4
Applying algebraic manipulation before solving trigonometric equations
Why This Matters
Solving trigonometric equations is essential for modeling periodic phenomena like waves, oscillations, and rotational motion. You'll use these techniques throughout physics, engineering, and advanced math courses including calculus and differential equations.
Before You Start — Make Sure You Can:
This Unit Includes
8 Video lessons
Practice exercises
Learning resources
Skills
Trigonometric Equations
Reference Angles
Quadrant Analysis
General Solutions
Special Triangles
Inverse Trigonometric Functions
Radian and Degree Conversion
NS Curriculum Aligned