Chapter 6: Trigonometric Functions: Right Triangle Approach

Chapter 6 connects angles to ratios of sides in triangles, then extends those ideas to any angle. You'll learn to measure angles in radians, use SOH-CAH-TOA, work with any angle (not just acute ones), use inverse trig to find angles, and apply the Law of Sines and Cosines to solve real triangles.

Textbook alignment

📘Stewart: ~Ch 6

📗Blitzer: ~Ch 4

📙Sullivan: ~Ch 6

📕Larson: ~Ch 4

📓OpenStax: ~Ch 6

Sections

6.1Angle Measure

Angles can be measured in degrees (familiar) or radians (what calculus needs). This section builds the bridge between the two and introduces arc length and sector area formulas.

RadianDegreeArc lengthSector+2 more

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5 concepts4 worked examples10 practice problems

6.2Trigonometry of Right Triangles

SOH-CAH-TOA is the foundation. This section defines the six trig ratios for acute angles, introduces the two special triangles you need to memorize, and shows how to find missing sides and angles.

Sine (sin)Cosine (cos)Tangent (tan)Cosecant (csc)+5 more

Study

5 concepts4 worked examples10 practice problems

6.3Trigonometric Functions of Angles

SOH-CAH-TOA only works for acute angles. This section extends trig to ANY angle by placing the angle in a coordinate system and using the point (x, y) on the terminal side. Reference angles make evaluating non-acute angles manageable.

Standard positionTerminal sideReference angleQuadrantal angle+1 more

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4 concepts3 worked examples10 practice problems

6.4Inverse Trigonometric Functions and Right Triangles

Inverse trig functions answer the question 'given a ratio, what is the angle?' They have restricted domains so the output is always a single angle (in a specific range). This section also covers solving right triangles completely.

Inverse sine (sin⁻¹ or arcsin)Inverse cosine (cos⁻¹ or arccos)Inverse tangent (tan⁻¹ or arctan)Solving a triangle

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2 concepts2 worked examples10 practice problems

6.5The Law of Sines

When triangles aren't right triangles, you need other tools. The Law of Sines handles AAS and ASA cases cleanly. The tricky SSA case (ambiguous case) can give 0, 1, or 2 solutions — this section teaches you to handle all of them.

Law of SinesAASASASSA (ambiguous case)

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2 concepts2 worked examples10 practice problems

6.6The Law of Cosines

The Law of Cosines handles the cases Law of Sines can't: SAS (two sides and the included angle) and SSS (all three sides). It's a generalization of the Pythagorean theorem. Heron's formula, derived from it, gives area from three sides.

Law of CosinesSASSSSHeron's Formula

Study

3 concepts2 worked examples10 practice problems

What's included — free

✓Visual concept explanations with diagrams for every section
✓Step-by-step worked examples you can study at your pace
✓Key vocabulary and memory aids for each topic
✓Printable worksheets generated for each section

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← Ch 5: Trigonometric Functions: Unit Circle Approach Ch 7: Analytic Trigonometry →