ITF - Inverse Trigonometric Functions Module Overview

Inverse Trigonometric Functions Module Overview

Now that you have explored the Unit Circle, common trigonometric ratios and how to graph the functions of sine, cosine and tangent, we will explore the inverse functions. The inverse functions can help us solve equations and use sinusoidal equations in real-world applications!

Essential Questions

How does symmetry help us extend our knowledge of the Unit Circle to an infinite number of angles?
How do I utilize technology to find all solutions for a trig equation?
How do inverse trigonometric functions help us solve equations?

Inverse Trigonometric Functions Key Terms

The following key terms will help you understand the content in this module.

Sinusoidal Function - A function is considered sinusoidal if its graph has a shape of equation image indicator $LaTeX: y=\sin x$ $y=\sin x$ or a transformation of $LaTeX: y=\sin x$ $y=\sin x$ . A cosine curve is also considered to be sinusoidal since a cosine function can be written in terms of sine.

Co-Terminal Angles - Two angles are co-terminal if they are drawn in standard position and their terminal sides are in the same location.

Even Functions - A function f is even if the graph of f is symmetric with respect to the y-axis. Algebraically, f is even if and only if equation image indicator $LaTeX: f\left(-x\right)=f\left(x\right)$ $f\left(-x\right)=f\left(x\right)$ for all x in the domain of f.

Odd Functions - A function f is even if the graph of f is symmetric with respect to the origin. Algebraically, f is odd if and only if equation image indicator $LaTeX: f\left(-x\right)=-f\left(x\right)$ $f\left(-x\right)=-f\left(x\right)$ for all x in the domain of f.

Reference Angle - A reference angle for angle is the positive acute angle made by the terminal side of the reference angle and the x -axis.

Inverse Function - An inverse function is a function that undoes the action of another function. A function g is the inverse of a function f if whenever y then x. In other words, applying f and then g is the same thing as doing nothing.

Negative Angles - A negative angle is created by rotating clockwise around the origin of a coordinate system, starting at the x-axis (the horizontal axis) and proceeding through the quadrants in the order IV, III, II, I.

Positive Angles - A positive angle is created by rotating counter-clockwise around the origin of a coordinate system, starting at the x-axis (the horizontal axis) and proceeding through the quadrants in the order I, II, III, IV.

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