# Trigonometric functions and exact value

Mnemonics[ edit ] Equivalent to the right-triangle definitions, the trigonometric functions can also be defined in terms of the rise, run, and slope of a line segment relative to horizontal. The three main trigonometric functions are commonly taught in the order sine, cosine and tangent. With a line segment length of 1 as in a unit circlethe following mnemonic devices show the correspondence of definitions:

As shown below, we will restrict the domains to certain quadrants so the original function passes the horizontal line test and thus the inverse function passes the vertical line test. Also note that the —1 is not an exponent, so we are not putting anything in a denominator.

These are called domain restrictions for the inverse trig functions. There is a subtle distinction between finding inverse trig functions and solving for trig functions. Graphs of Inverse Trig Functions Here are tables of the inverse trig functions and their t-charts, graphs, domain and range also called the principal interval.

First, inverse sin and inverse cos: Here are the inverse tan and cot functions. Notice that the tan and cot inverse functions come from different sets of quadrants: And here are the inverse csc and sec functions: Here is the Unit Circle again: In the degrees mode, you will get the degrees.

Here are more problems: Now we will transform the Inverse Trig Functions. T-Charts for the Six Inverse Trigonometric Functions Some prefer to do all the transformations with t-charts like we did earlier, and some prefer it without t-charts; most of the examples will show t-charts.

Here are the inverse trig parent function t-charts I like to use. Note that each is in the correct quadrants in order to make true functions. Here are examples, using t-charts to perform the transformations. Here are examples of reciprocal trig function transformations: We still have to remember which quadrants the inverse inside trig functions come from: I checked answers for the exact angle solutions.

The easiest way to do this is to draw triangles on they coordinate system, and if necessary use the Pythagorean Theorem to find the missing sides. Here are some problems where we have variables in the side measurements.

Learn these rules, and practice, practice, practice! Click on Submit the arrow to the right of the problem to solve this problem. You can also type in more problems, or click on the 3 dots in the upper right hand corner to drill down for example problems.

You can even get math worksheets. There is even a Mathway App for your mobile device. Welcome to She Loves Math! And, even better, a site that covers math topics from before kindergarten through high school.Sep 29,  · Mr.

Kiker explains how to evaluate the exact values of inverse trigonometric functions. math — Mathematical functions¶. This module is always available.

It provides access to the mathematical functions defined by the C standard. These functions cannot be used with complex numbers; use the functions of the same name from the cmath module if you require support for complex numbers. The distinction between functions which support complex numbers and those which don’t is.

Exact Values of the Trigonometric Functions Test yourself on the exact values of the six trigonometric functions at the "nice" angles. Click on "Show" and "Hide" in . Trigonometry Examples.

## SparkNotes: Trigonometry: Trigonometric Functions: Reference Angles

Step-by-Step Examples. Trigonometry. Simplifying Trigonometric Expressions. Find the Exact Value.

Find an angle that is coterminal to. Tap for more steps Subtract from. The resulting angle of .

## Exact Trig Values

Trigonometric Functions and Right Triangles. Find the exact values of the six trigonometric functions of the angle $$\theta$$.

Solution. When it says “exact value”, it means that you should not give a decimal approximation. This means that once you get a simplified fraction, you will leave the answer as it is.

Calculate sine, cosine, tangent, cotangent, secant and cosecant for values in degrees or radians. Trigonometric or circular functions calculator for degrees or radians. Graphs of trigonometric functons. Calculate sine, cosine, tangent, cotangent, secant and cosecant for values in degrees or radians.

The trigonometric functions are also.

Trigonometry Examples | Simplifying Trigonometric Expressions | Finding the Exact Value