Common Core · High school
HSF-TF.A.4
High school — Use the unit circle to explain the symmetry and periodicity of the trigonometric functions.
A note on this mapping: The quotient and reciprocal identities have no standard of their own; the Common Core treats them as definitions used inside HSF-TF.C.8. HSF-TF.A.4 is a (+) standard.
The 2 skills that cover it
- Trigonometric IdentitiesUse the Pythagorean and quotient identities to simplify expressions and verify equations.Read the lesson →
- Graphs of Sine & CosineUnroll the unit circle into a wave: read the amplitude, period, midline and phase shift of y = a sin(b(x - h)) + k off its equation and its graph, and write the equation of a wave you are shown.Read the lesson →
What a student should be able to do
- Apply sin2 t + cos2 t = 1 and its rearrangements.
- Use the quotient and reciprocal identities.
- Simplify a trigonometric expression to a single function.
- Verify an identity step by step.
- State the amplitude, period and midline of a sine or cosine function from its equation.
- Find the phase shift and the direction of a reflection.
- Write the equation of a sine or cosine wave from its features or its graph.
- Model a periodic situation, such as a tide or a wheel, with a sinusoidal function.