Trigonometric identities and equations

OpenStax

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Introduction to trigonometric identities and equations

Solving trigonometric equations with identities

1 Verifying the fundamental trigonometric identities

2 Using algebra to simplify trigonometric expressions

3 Key equations

5 Section exercises

Sum and difference identities

1 Using the sum and difference formulas for cosine

2 Using the sum and difference formulas for sine

3 Using the sum and difference formulas for tangent

4 Using sum and difference formulas for cofunctions

5 Using the sum and difference formulas to verify identities

6 Key equations

8 Section exercises

Double-angle, half-angle, and reduction formulas

1 Using double-angle formulas to find exact values

2 Using double-angle formulas to verify identities

3 Use reduction formulas to simplify an expression

4 Using half-angle formulas to find exact values

5 Key equations

7 Section exercises

Sum-to-product and product-to-sum formulas

1 Expressing products as sums

2 Expressing products as sums for cosine

3 Expressing the product of sine and cosine as a sum

4 Expressing products of sines in terms of cosine

5 Expressing sums as products

6 Key equations

8 Section exercises

Solving trigonometric equations

1 Solving linear trigonometric equations in sine and cosine

2 Solving equations involving a single trigonometric function

3 Solve trigonometric equations using a calculator

4 Solving trigonometric equations in quadratic form

5 Solving trigonometric equations using fundamental identities

6 Solving trigonometric equations with multiple angles

7 Solving right triangle problems

9 Section exercises

15 Real-world applications

Modeling with trigonometric equations

1 Determining the amplitude and period of a sinusoidal function

2 Finding equations and graphing sinusoidal functions

3 Modeling periodic behavior

4 Modeling harmonic motion functions

5 Simple harmonic motion

6 Damped harmonic motion

7 Bounding curves in harmonic motion

8 Key equations

10 Section exercises

15 Real-world applications

17 Chapter review exercises

18 Solving Trigonometric Equations with Identities

19 Sum and Difference Identities

20 Double-Angle, Half-Angle, and Reduction Formulas

21 Sum-to-Product and Product-to-Sum Formulas

22 Solving Trigonometric Equations

23 Modeling with Trigonometric Equations

24 Practice test

Source: OpenStax, Precalculus. OpenStax CNX. Jan 19, 2016 Download for free at https://legacy.cnx.org/content/col11667/1.6

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