Curriculum placement
Precalculus. This describes the skill, not a learner estimate.
Solving trigonometric equations
Solve trigonometric equations on specified intervals
Problem types
- Solve trigonometric equations
- Set up and solve with an inverse function
- All solutions on the model's domain
- Interpret the solutions of a model
Builds on
- Inverse trigonometric functions
- Pythagorean and angle-sum identities
- Odd, even, and periodic trig functions · Useful idea
Symmetry of the unit circle gives a second solution of a trigonometric equation in each period.
- Approximating a solution from a graph · Useful idea
The solutions of a trigonometric equation are the points where the sine graph meets a horizontal line, so there are many of them.
Leads to
- The complex plane · See it applied
Finding the angles whose cosine and sine match the parts of a complex number solves a trigonometric equation.
- The laws of sines and cosines · See it applied
Finding an angle of a triangle from the law of sines solves an equation in the sine, which can have two solutions.
- Choosing a periodic model · See it applied
Setting a sinusoidal model equal to a value and solving gives the times at which the modeled quantity reaches that value.
Related skills
- Solving exponential and logarithmic equations · Related idea
Solving for an unknown exponent and solving for an unknown angle both apply an inverse function to isolate the variable.
Open the interactive map to explore lessons and skill connections.