Inverse Trigonometric Functions
This page focuses on inverse trigonometric functions, which are essential when solving for missing angles in right triangles. It explains how to use these functions and provides practical examples.
Definition: Inverse trigonometric functions, also known as arcfunctions, are used to find an angle when given a trigonometric ratio.
The three main inverse trigonometric functions are:
- Inverse Sine (Sin⁻¹ or arcsin)
- Inverse Cosine (Cos⁻¹ or arccos)
- Inverse Tangent (Tan⁻¹ or arctan)
Highlight: When using a calculator for inverse trig functions, look for the "second function" or "shift" key to access these operations.
The page provides formulas for each inverse function:
• Sin⁻¹(θ) = opposite / hypotenuse
• Cos⁻¹(θ) = adjacent / hypotenuse
• Tan⁻¹(θ) = opposite / adjacent
Example: To find a missing angle in a right triangle with an opposite side of 7 and a hypotenuse of 39:
θ = Sin⁻¹(7/39)
θ ≈ 15°
The page includes additional examples for inverse cosine and inverse tangent, demonstrating how to use inverse trig functions step by step.
Vocabulary: Hypotenuse - The longest side of a right triangle, opposite the right angle.
These examples illustrate how to apply inverse trigonometric functions to solve for missing angles in right triangles, which is a fundamental skill in trigonometry and has applications in various fields such as physics, engineering, and navigation.
