Trigonometry study guide
This guide is designed to help you understand the core ideas that commonly appear in introductory college Trigonometry courses. Read the explanation, follow the example, then try the practice questions without looking back. The goal is to understand the reasoning—not just memorize an answer.
Course requirements vary by school and instructor. Use this as a learning and review resource alongside your assigned textbook, lectures, and instructor guidance.
Right-triangle ratios
Concept: SOH-CAH-TOA defines sine, cosine, and tangent as side ratios in right triangles.
Worked example: If opposite=3 and hypotenuse=5, sin θ=3/5.
Remember: Focus on the central relationship in right-triangle ratios, define the important terms, and connect each step to the evidence, rule, formula, or process being used.
Common mistakes: Common mistakes include memorizing right-triangle ratios without understanding when it applies, skipping units or definitions, and giving an answer without showing the reasoning that supports it.
Practice it
- Explain right-triangle ratios in your own words.
- Use the lesson idea to create or solve one new trigonometry example.
- What is one common mistake a student should avoid when working with right-triangle ratios?
Unit circle
Concept: The unit circle gives exact sine and cosine values for standard angles and all quadrants.
Worked example: At π/2, the point is (0,1), so cos=0 and sin=1.
Remember: Focus on the central relationship in unit circle, define the important terms, and connect each step to the evidence, rule, formula, or process being used.
Common mistakes: Common mistakes include memorizing unit circle without understanding when it applies, skipping units or definitions, and giving an answer without showing the reasoning that supports it.
Practice it
- Explain unit circle in your own words.
- Use the lesson idea to create or solve one new trigonometry example.
- What is one common mistake a student should avoid when working with unit circle?
Trig identities
Concept: Identities such as sin²x+cos²x=1 let you rewrite and simplify trigonometric expressions.
Worked example: If sin x=3/5 in quadrant I, cos x=4/5.
Remember: Focus on the central relationship in trig identities, define the important terms, and connect each step to the evidence, rule, formula, or process being used.
Common mistakes: Common mistakes include memorizing trig identities without understanding when it applies, skipping units or definitions, and giving an answer without showing the reasoning that supports it.
Practice it
- Explain trig identities in your own words.
- Use the lesson idea to create or solve one new trigonometry example.
- What is one common mistake a student should avoid when working with trig identities?
Solving trig equations
Concept: Trig equations can have many solutions because trig functions repeat.
Worked example: sin x=0 on 0≤x<2π at x=0 and x=π.
Remember: Focus on the central relationship in solving trig equations, define the important terms, and connect each step to the evidence, rule, formula, or process being used.
Common mistakes: Common mistakes include memorizing solving trig equations without understanding when it applies, skipping units or definitions, and giving an answer without showing the reasoning that supports it.
Practice it
- Explain solving trig equations in your own words.
- Use the lesson idea to create or solve one new trigonometry example.
- What is one common mistake a student should avoid when working with solving trig equations?
Law of sines & cosines
Concept: These laws solve non-right triangles using side-angle relationships.
Worked example: The Law of Cosines generalizes the Pythagorean theorem: c²=a²+b²−2ab cos C.
Remember: Focus on the central relationship in law of sines & cosines, define the important terms, and connect each step to the evidence, rule, formula, or process being used.
Common mistakes: Common mistakes include memorizing law of sines & cosines without understanding when it applies, skipping units or definitions, and giving an answer without showing the reasoning that supports it.
Practice it
- Explain law of sines & cosines in your own words.
- Use the lesson idea to create or solve one new trigonometry example.
- What is one common mistake a student should avoid when working with law of sines & cosines?