Trigonometry

Angles, Triangles, Ratios & the Unit Circle

📚 Grade 7–8 / Advanced 6 Units 30 Weeks 150 Lessons 🔴 Advanced

The math of angles and waves. Trigonometry connects geometry and algebra through the relationships between sides and angles of triangles. From the Pythagorean Theorem to sine, cosine, and tangent — then on to the unit circle and identities — this volume unlocks a whole new dimension of mathematical thinking.

Units

Weeks

150

Lessons

Gr. 7–8 / Adv.

Level

Unit Tests

What You Will Learn in Volume 4

📐

Right Triangles

📊

sin / cos / tan

🔺

Special Triangles

⭕

The Unit Circle

📈

Trig Graphs

🔗

Trig Identities

Volume 4 — Full Unit Breakdown

Click any unit to see all weekly topics and lessons

Week 1

Right Triangle Review

• Parts of a right triangle
• Legs & hypotenuse
• Right angle symbol
• Identifying right triangles
• Real-world right triangles

Week 2

Pythagorean Theorem

• a² + b² = c²
• Finding the hypotenuse
• Finding a missing leg
• Pythagorean triples
• Checking right triangles

Week 3

Applying the Theorem

• Distance between points
• Diagonal of a rectangle
• Height of a triangle
• 3D applications
• Real-world word problems

Week 4

Similar Right Triangles

• Similar triangles review
• Ratios of sides
• Altitude to hypotenuse
• Geometric mean
• Applications

★ Week 5

Unit 1 Review & Test

• Review right triangles
• Review Pythagorean Theorem
• Mixed applications
• Challenge problems
• ★ Unit 1 Test

Week 6

Sine

• Opposite & hypotenuse
• sin θ = opp/hyp
• Finding sine values
• Using a calculator
• Sine in triangles

Week 7

Cosine

• Adjacent & hypotenuse
• cos θ = adj/hyp
• Finding cosine values
• Sine vs. cosine
• Cosine in triangles

Week 8

Tangent

• Opposite & adjacent
• tan θ = opp/adj
• Finding tangent values
• SOH CAH TOA memory
• All three ratios

Week 9

Inverse Trig Functions

• arcsin / sin⁻¹
• arccos / cos⁻¹
• arctan / tan⁻¹
• Finding missing angles
• Real-world applications