Lesson 7.1
Law of Sines and Law of Cosines
Pair each side with its opposite angle. The law of cosines handles SAS and SSS; the law of sines handles known opposite pairs. A computed inverse sine may require checking a second possible angle.
← Precalculus Study Guide
Unit 7
Analytic and Applied Trigonometry
Triangles that are not right-angled, and the inverse functions that recover an angle. Choosing the correct law from the given parts is most of the work.
Lessons and exercises
Lesson 7.2
The Ambiguous Case
With SSA data and an acute known angle, a side can reach a ray at zero, one, or two points. After an inverse-sine calculation, test the supplementary angle and verify the angle sum. A sine value greater than one means no triangle.
Lesson 7.3
Inverse Trigonometric Functions
Inverse trigonometric functions return principal angles in restricted ranges. Arcsine returns angles from minus pi/2 to pi/2, arccosine from zero to pi, and arctangent from minus pi/2 to pi/2 excluding endpoints. They do not undo a trig function on every real angle.
Need help with this topic?
Work through questions with a tutor and get help with the steps you find difficult.
Get help with this topic