Common Core · High school
HSF-TF.B.7
High school — Use inverse functions to solve trigonometric equations that arise in modelling contexts; evaluate the solutions using technology, and interpret them in terms of the context.
A note on this mapping: HSF-TF.B.7 is a (+) standard — beyond the college- and career-ready threshold, i.e. precalculus rather than Algebra II.
The 2 skills that cover it
- 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 →
- Inverse Trigonometric FunctionsGo from a ratio back to an angle, carefully: exact values of arcsin, arccos and arctan, the restricted ranges that make them functions, compositions such as sin(arccos x), calculator values, and the angle a situation asks for.Read the lesson →
What a student should be able to do
- 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.
- Evaluate arcsin, arccos and arctan exactly for the special ratios, in radians and degrees.
- State the domain and range of each inverse trigonometric function and explain why arcsin(sin t) is not always t.
- Evaluate a composition such as sin(arccos(3/5)) or tan(arcsin x) exactly.
- Use an inverse trigonometric function to find the angle in an applied problem or an equation.