- Trigonometry
- Angles in Standard Positions
- Coterminal Angles
- Angle Conversion
- Origins of Trigonometry
- Trigonometric Ratios
- Solving a Right-Angle Trigonometry Question
- Pythagorean Theorem
- Inverse Trigonometric Functions
- Trigonometric Circle
- Sine and Cosine Law
- Simplifying Trigonometric Expressions
- Graphing Trigonometric Functions
- Proving Trigonometric Identities

Simplifying trigonometric expressions can be helpful when we are solving trigonometric equations or proving trigonometric identities. We can use the basic trigonometric ratios, combined and double-angle formulas, as well as reciprocal and other identities to do so.

The following are common formulas and identities we can use as tools to simplify trigonometric expressions:

(Source: https://www.onlinemathlearning.com/image-files/trigonometric-identities.png)

Watch this video for proofs of the Pythagorean Identities:

You can use the information on the following image to remember the combined angle formulas:

See this video where we review the basic trigonometric ratios and identities that we can use to simplify trigonometric expressions, as well as solutions to the following example:

1. \((sin\theta\cdot tan\theta)(csc\theta+cot\theta)\) (starts at 1:59) | 2. \(\frac{tan(x)\cdot csc^2(x)}{1+tan^2(x)}\) (starts at 3:35) |

See this video where we review the combined angle formulas that we can use to simplify trigonometric expressions, as well as solutions to the following example:

1. \(sin3x\cdot cosx-sinx\cdot cos3x\) (starts at 5:09) | 2.\(cos(x+\pi)\cdot cos(x-\pi)+sin(x+\pi)\cdot sin(x-\pi)\) (starts at 6:03) |

- Last Updated: Apr 11, 2023 5:52 PM
- URL: https://libraryguides.centennialcollege.ca/c.php?g=716824
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