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Fall 2026 · Prof. Young & Prof. Volk

Math 130 — Test 3 Review

Sections 5.1 to 5.3, 5.7, 7.1, and 8.4: trigonometry, right-triangle applications, and vectors. Dates and deadlines are on the MATH 130 page.

Start here · Unit 3 pathway

Bridge → learn → practice → checkpoint

Start with the Unit 3 bridge, build trigonometry before applications, then learn vectors, and finish with mixed Test 3 review.

Step 1 · Units 3A and 3B · Quiz 10

Angles, trig foundations, and reference angles

Work through 3A before 3B. Build angle and triangle fluency first, then use reference angles, signs, and exact trig values.

Learn with 3A Continue with 3B
Step 2 · Unit 3C · Quiz 11

Right-triangle applications

Translate diagrams and contexts into right triangles, then practice elevation, bearings, motion, and multi-step applications.

Learn with 3C
Step 3 · Unit 3D · Quiz 12

Vectors

Focus on components, graph/resultant vectors, magnitude, and direction. Keep one earlier trig retrieval problem in each study session.

Learn with 3D
Step 4 · Unit 3E · Quiz 13 and Test 3

Cumulative Test 3 readiness

Quiz 13 is a cumulative readiness check, not new content. Use it to find and fix weak areas before Test 3.

Review with 3E

Readiness rule: Reach at least 80%, correct every missed setup, and revisit the matching deck before retrying. Start reviewing for the final exam here.

Deck library and downloadable files
Formula priorities

Essential Formulas for Test 3

Prefer a walkthrough? Jump to the study videos.

Memorize
Provided on Test 3
Useful relation

Current Test 3 Review Formula Reference

Provided on Test 3
Pythagorean Identity
$$\sin^2 x + \cos^2 x = 1$$
Use to connect sine and cosine values.
Provided on Test 3
Tangent/Secant Identity
$$1 + \tan^2 x = \sec^2 x$$
Use when tangent or secant is known and you need the other.
Provided on Test 3
Area of a Triangle (SAS form)
$$\text{Area} = \frac{1}{2}bc\sin A$$
Use when two sides and the included angle are given.

Section 5.1–5.2 Foundations

Memorize
Arc Length
$$s=r\theta$$ $$s=\frac{\theta}{360}(2\pi r)$$
Use radian form when $\\theta$ is in radians, degree form when in degrees.
Memorize
Right-Triangle Ratios
$$\sin\theta=\frac{\text{opp}}{\text{hyp}}$$
$$\cos\theta=\frac{\text{adj}}{\text{hyp}}$$
$$\tan\theta=\frac{\text{opp}}{\text{adj}}$$
Core relationships for side/angle solving in right triangles.
Useful
Coterminal Angles
$$\theta_{\text{coterminal}} = \theta + 360^\circ k \quad \text{or} \quad \theta + 2\pi k$$
Use integer $k$ to generate coterminal angles in degrees or radians.

Section 5.3 & 7.1 Applications

Memorize
Reference Angle by Quadrant
$$QII:\ \alpha=180^\circ-\theta$$
$$QIII:\ \alpha=\theta-180^\circ$$
$$QIV:\ \alpha=360^\circ-\theta$$
Use degree equivalents with $\pi$ for radian forms.
Memorize
Distance-Rate-Time
$$d=rt$$
Used with trig setup in many Section 7.1 word problems.
Memorize
Solve Right Triangle via Inverse Trig
$$\theta=\sin^{-1}\!\left(\frac{\text{opp}}{\text{hyp}}\right)$$
$$\theta=\cos^{-1}\!\left(\frac{\text{adj}}{\text{hyp}}\right)$$
$$\theta=\tan^{-1}\!\left(\frac{\text{opp}}{\text{adj}}\right)$$
Pick the inverse function matching known sides.

Section 8.4 Vectors

Memorize
Component Form from Points
$$\vec v=\langle x_2-x_1,\ y_2-y_1\rangle$$
From initial point $(x_1,y_1)$ to terminal point $(x_2,y_2)$.
Memorize
Vector Magnitude
$$|\vec v|=\sqrt{a^2+b^2}\quad \text{for }\vec v=\langle a,b\rangle$$
Length of a vector in component form.
Memorize
Direction Angle
$$\theta=\tan^{-1}\!\left(\frac{b}{a}\right)$$
Adjust for quadrant when determining the final direction angle.
Useful
Vector from Magnitude & Direction
$$\vec v=\langle |\vec v|\cos\theta,\ |\vec v|\sin\theta\rangle$$
Useful when converting directional information to components.
Interactive review

Practice Generators

🎯 Quiz 13 / Test 3 Readiness Check

20 mixed Unit 3 review questions from Sections 5.1, 5.2, 5.3, 5.7, 7.1, and 8.4. Confirm the official Fall test coverage and formula sheet in Canvas or in class.

📝 Mock Quiz Mode

Quizzes 10 to 12 check each step of Unit 3, and Quiz 13 is a cumulative readiness check for Test 3. Dates are on the MATH 130 page.

Trig & Vector Practice Tools

Extra practice for Sections 5.3, 7.1 & 8.4

Interactive drills for the trickiest Unit 3 skills — angles, right-triangle applications, and vectors.

Quiz 10 Notes + Practice (Section 5.3)

A printable reference-angle notes sheet and a dedicated practice set for the planned Quiz 10 skills.

Open Quiz 10 Practice Printable Notes

Skyhawk Trig (Section 7.1)

A flight-themed game drilling right-triangle and angle-of-elevation skills.

Play Skyhawk Trig

Vector Masterclass

An interactive lesson and worksheet walkthrough of components, magnitude, and direction.

Open Vector Masterclass

Vector Gap Review

A slide-deck walkthrough that closes common gaps on vector problems, with companion notes.

Open review deck Guided notes

Study Videos

The Unit 3 videos are being re-linked. Until they are posted, use the Unit 3 slides on the MATH 130 page and the practice in this review.

Study progress

Topics Checklist

Use the progress bars as your top-level map, then work through each checklist group below so dense topic lists feel subordinate to the overall study plan.

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