Evaluating sin(π/3) and cos(5π/4)

Trigonometry · Axiom Academy

EXAMPLE Evaluating Trigonometric Functions Use the unit circle to evaluate sin(π/3) and cos(5π/4) step-by-step Excellent work! You've learned to evaluate trigonometric functions using the unit circle. Here's what to remember: Identify the quadrant: Use the angle's value to determine which quadrant it falls in (I, II, III, or IV) Find the reference angle: For angles beyond the first quadrant, calculate the reference angle to help find coordinates Determine coordinates: Find the (x, y) coordinates on the unit circle for that angle, paying attention to signs based on the quadrant Extract the value: sin(θ) = y-coordinate, cos(θ) = x-coordinate, tan(θ) = y/x Quadrant signs matter: In Q1: both positive; Q2: sin positive, cos negative; Q3: both negative; Q4: cos positive, sin negative The unit circle is a powerful tool for evaluating any trigonometric function. Master the key angles (0, π/6, π/4, π/3, π/2) and their coordinates, and you can evaluate trig functions anywhere on the circle!

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