Trigonometry · Honors

High school · Math

Curriculum programs

Click a standard for the full text and study materials.

1.1 — Angles in degrees and radians. Measure angles in standard position; convert between degrees and radians.
1.2 — Right triangle trigonometry. Define sin, cos, tan for acute angles; solve right triangles.
1.3 — The unit circle. Evaluate sine and cosine using the unit circle and reference angles.
1.4 — Define csc, sec, and cot. Define cosecant, secant, and cotangent as reciprocal or quotient trigonometric functions.
1.5 — Relate reciprocal functions to sin, cos, and tan. Relate cosecant, secant, and cotangent to sine, cosine, and tangent.

2.1 — Graph y = A sin(Bx − C) + D. Graph y = A sin(Bx − C) + D by identifying its amplitude, period, phase shift, and vertical shift.
2.2 — Cosine transformations. Graph transformed cosine functions using amplitude, period, phase shift, and vertical shift.
2.3 — Graph tangent, cotangent, and secant. Graph tangent, cotangent, and secant functions with their periods and asymptotes.
2.4 — Graph cosecant with asymptotes. Graph cosecant functions by using reciprocal relationships and vertical asymptotes.
2.5 — Inverse trigonometric functions. Define and use arcsin, arccos, arctan with appropriate ranges.

3.1 — Verifying identities. Simplify and verify trig identities using fundamental relationships.
3.2 — Apply sine and cosine addition formulas. Use angle-addition and angle-subtraction formulas to evaluate sine and cosine.
3.3 — Tangent addition formulas. Use angle-addition and angle-subtraction formulas to evaluate tangent.
3.4 — Use double-angle and half-angle identities. Apply double-angle and half-angle identities to evaluate and simplify trigonometric expressions.
3.5 — Reduction formulas. Use reduction formulas to rewrite trigonometric functions of related angles.
3.6 — Apply product-to-sum identities. Use product-to-sum identities to rewrite products of trigonometric functions as sums.
3.7 — Sum-to-product identities. Use sum-to-product identities to rewrite sums or differences of trigonometric functions.
3.8 — Solve trig equations on a restricted domain. Solve trigonometric equations over a specified restricted interval.
3.9 — General solution sets. Express all solutions of trigonometric equations using general solution forms.
3.10 — Proof-oriented identity work. Prove multi-step identities with clear justifications at each step.

4.1 — Solve oblique triangles with AAS and ASA. Use the Law of Sines to solve oblique triangles given AAS or ASA information.
4.2 — SSA (ambiguous case). Use the Law of Sines to determine the possible triangles in the SSA ambiguous case.
4.3 — Solve oblique triangles with SAS. Use the Law of Cosines and Law of Sines to solve oblique triangles given SAS information.
4.4 — Solve SSS triangles. Use the Law of Cosines to solve oblique triangles given three side lengths.
4.5 — Plot points in polar form. Plot polar coordinates and identify equivalent representations of the same point.
4.6 — Polar and rectangular forms. Convert points and equations between polar and rectangular coordinate forms.
4.7 — Represent vectors. Represent vectors geometrically and in component form using magnitude and direction.
4.8 — Operate on vectors in the plane. Add, subtract, and scale vectors in the coordinate plane.
4.9 — Polar form of complex numbers. Write complex numbers in polar form; multiply and divide using moduli and arguments.
4.10 — Eliminate parameters. Eliminate a parameter to convert parametric equations into a rectangular equation.
4.11 — Graph simple parametric curves. Graph simple parametric curves and identify their orientation and rectangular equations.