Common Core · High school
HSF-TF.A.2
High school — Explain how the unit circle extends sine and cosine to all real numbers, traced counterclockwise.
The 2 skills that cover it
- The Unit CircleExtend sine and cosine to all angles using coordinates on the unit circle, and read exact values off it.Read the lesson →
- Trigonometric EquationsFind every angle that makes a trigonometric equation true: isolate the ratio, read the reference angle off the unit circle, place it in the right quadrants, and use an identity or a substitution when the equation is quadratic.Read the lesson →
What a student should be able to do
- Give exact sine and cosine for the special angles.
- Use reference angles and quadrant signs.
- Relate coordinates on the unit circle to (cos t, sin t).
- Evaluate trig functions of angles beyond one full turn.
- Solve a basic trigonometric equation on a given interval.
- Solve an equation that needs factoring or a quadratic substitution.
- Use an identity to rewrite an equation in one ratio before solving.
- Solve an equation with a multiple angle, and write the general solution.