Free ebook on trigonometry covering angles, right triangles, the unit circle, graphs, and core identities with visual reasoning.
Free ebook content
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Angles in Trigonometry: Degrees, Radians, and Rotation
+ Exercise: Which statement correctly explains why the formula s = rθ requires θ to be measured in radians?
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Right-Triangle Trigonometry: Sine, Cosine, and Tangent
+ Exercise: In a right triangle, tan(θ) = 3/4 for one acute angle θ. What is the tangent of the other acute angle in the same triangle?
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Solving Real Right-Triangle Problems: Ramps, Shadows, and Bearings
+ Exercise: A boat travels 12.0 km on a bearing of N 25° E. Which equations correctly find how far north and how far east it traveled?
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Special Right Triangles and Special Angles in Trigonometry
+ Exercise: In a 30-60-90 right triangle, the hypotenuse is 10. What are the exact lengths of the short leg (opposite 30°) and the long leg (opposite 60°)?
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The Unit Circle: Coordinates as Cosine and Sine
+ Exercise: A point on the unit circle is (x, y) = (0.6, 0.8). Which statement correctly identifies cos θ and sin θ?
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From Unit Circle to Graphs: Basic Sine and Cosine Patterns
+ Exercise: Which statement correctly describes the key features of y = cos θ over one period from 0 to 2π?
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Core Trigonometric Identities: Pythagorean and Simple Ratio Relationships
+ Exercise: Which approach is recommended for verifying a trigonometric identity without making invalid steps?
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Putting It Together: Mixed Trigonometry Skills with Visual Reasoning
+ Exercise: A drone travels 120 m at an angle of 28° above the horizontal. Which setup correctly finds the horizontal distance x and the altitude gain y?
About the free ebook
Trigonometry Without Fear: Angles, Triangles, and the Unit Circle
This free online ebook makes trigonometry approachable through visual reasoning, practical examples, and the key relationships that connect angles, triangles, circles, and graphs.
Build confidence with essential trigonometry
Learn how degrees and radians describe rotation, then use sine, cosine, and tangent to connect angle measures with side lengths in right triangles. Clear explanations help turn formulas into useful tools rather than rules to memorize.
Apply trigonometry to realistic situations
Explore how trigonometric ratios can model heights, ramps, shadows, distances, and bearings. Special triangles and familiar angle values provide efficient ways to solve problems while strengthening number sense.
Connect the unit circle, graphs, and identities
See why cosine and sine are coordinates on the unit circle and how those coordinates create repeating graph patterns. The ebook also introduces core identities, including the Pythagorean identity, so you can verify relationships and solve mixed problems with greater accuracy.
What you will practice
- Converting and interpreting degrees and radians
- Choosing sine, cosine, or tangent for a right-triangle problem
- Using special-angle values and unit-circle coordinates
- Reading basic sine and cosine behavior
- Combining diagrams, ratios, and identities to reason through problems
Designed for school learners who want a calmer path into trigonometry, this ebook emphasizes understanding before memorization.
How do degrees and radians relate in trigonometry?
They measure the same angle in different units: 180 degrees equals π radians.
When should I use sine, cosine, or tangent?
Use the ratio that connects the known side and needed side relative to the chosen angle.
Why are sine and cosine coordinates on the unit circle?
For an angle on a circle of radius 1, the point coordinates are cosine for x and sine for y.
This ebook includes:
8 content chapters
Digital certificate of course completion (Free)
Exercises to train your knowledge
100% free, from content to certificate
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