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Chapter 10

Trigonometry

Book Version 13
By Boundless
Boundless Algebra
Algebra
by Boundless
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Section 1
Trigonometry and Right Triangles
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Right Triangles and the Pythagorean Theorem

The Pythagorean Theorem, ${\displaystyle a^{2}+b^{2}=c^{2},}$ can be used to find the length of any side of a right triangle.

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How Trigonometric Functions Work

Trigonometric functions can be used to solve for missing side lengths in right triangles.

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Sine, Cosine, and Tangent

The mnemonic SohCahToa can be used to solve for the length of a side of a right triangle.

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Finding Angles From Ratios: Inverse Trigonometric Functions

The inverse trigonometric functions can be used to find the acute angle measurement of a right triangle.

Section 2
Trigonometric Functions and the Unit Circle
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Radians

Radians are another way of measuring angles, and the measure of an angle can be converted between degrees and radians.

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Defining Trigonometric Functions on the Unit Circle

Identifying points on a unit circle allows one to apply trigonometric functions to any angle.

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Special Angles

The unit circle and a set of rules can be used to recall the values of trigonometric functions of special angles.

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Sine and Cosine as Functions

The functions sine and cosine can be graphed using values from the unit circle, and certain characteristics can be observed in both graphs.

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Tangent as a Function

Characteristics of the tangent function can be observed in its graph.

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Secant and the Trigonometric Cofunctions

Trigonometric functions have reciprocals that can be calculated using the unit circle.

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Inverse Trigonometric Functions

Each trigonometric function has an inverse function that can be graphed.

Section 3
Trigonometric Identities
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The Law of Sines

The law of sines can be used to find unknown angles and sides in any triangle.

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The Law of Cosines

The law of cosines can be used to solve for angles and sides of a triangle in cases where other laws do not apply.

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Pythagorean Identities

The Pythagorean identities are useful in simplifying expressions with trigonometric functions.

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Angle Addition and Subtraction Formulae

Trigonometric expressions can be simplified using special angles and a set of formulae for adding and subtracting angles.

Double and Half Angle Formulae

Trigonometric expressions can be simplified by applying the double- and half-angle formulae.

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Trigonometric Symmetry Identities

The trigonometric symmetry identities are based on principles of even and odd functions that can be observed in their graphs.

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Boundless Algebra by Boundless
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Matrices
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Chapter 10
Trigonometry
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Conic Sections
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