Solving sin(2x - π/3) = 1/2

Trigonometry · Axiom Academy

EXAMPLE Solving Trigonometric Equations Learn to find all solutions using inverse trig functions and general solution formulas Excellent work! You've successfully found all solutions to a trigonometric equation. Here's what we learned: Use Inverse Functions: Apply arcsin (or the unit circle) to find the principal value where sin(θ) equals the given value Find All Reference Angles: Remember that sine is positive in both Quadrant I and Quadrant II, so check for π - θ as well Apply General Solution Formula: Add 2πn (the period of sine) to account for the function's periodicity and find infinitely many solutions Solve for the Variable: Don't forget to isolate x by performing inverse operations (add, divide, etc.) on both families of solutions Express Complete Solutions: Your final answer should include both families of solutions and specify that n ∈ ℤ This systematic approach works for any trigonometric equation. Remember: find the principal value, identify all angles with that trig value, apply the periodicity, and solve for your variable. Master this pattern, and you'll be able to solve any trig equation!

This is the written version of the interactive lesson above. See the full Trigonometry course.