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:

1. Inverse Sine (Sin⁻¹ or arcsin)
2. Inverse Cosine (Cos⁻¹ or arccos)
3. 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.

Parts of a Right Triangle and Basic Trigonometric Functions

This page introduces the fundamental components of a right triangle and the basic trigonometric functions. It provides a clear visual representation of a right triangle, labeling its parts and explaining the relationships between them.

The three main parts of a right triangle are:

1. Opposite side (across from the angle)
2. Adjacent side (next to the angle)
3. Hypotenuse (longest side, across from the right angle)

Vocabulary: SOH CAH TOA - A mnemonic device used to remember the basic trigonometric functions: • Sine = Opposite / Hypotenuse • Cosine = Adjacent / Hypotenuse • Tangent = Opposite / Adjacent

The page also includes examples of how to use these basic trig functions explained with examples. For instance:

Example: To find the length of the opposite side (X) in a right triangle with a 37° angle and a hypotenuse of 10.3 units: Sin(37°) = X / 10.3 X = 10.3 * Sin(37°) X ≈ 6.2 units

Similar examples are provided for cosine and tangent functions, demonstrating how to calculate missing sides in a right triangle using trigonometric functions examples with solution.

Highlight: Understanding these basic trigonometric functions and their relationships to the parts of a right triangle is crucial for solving more complex trigonometry problems and applications in real-world scenarios.