Trigonometry Cheatsheet

Cheat Codes & Shortcuts

• Basic Functions: \( \sin \theta, \cos \theta, \tan \theta \)
• Reciprocal Functions: \( \csc \theta = \frac{1}{\sin \theta} \), \( \sec \theta = \frac{1}{\cos \theta} \), \( \cot \theta = \frac{1}{\tan \theta} \)
• Pythagorean Identities: \( \sin^2 \theta + \cos^2 \theta = 1 \)
• Angle Sum & Difference: \( \sin(a \pm b) = \sin a \cos b \pm \cos a \sin b \)
• Double Angle Formulas: \( \sin 2\theta = 2 \sin \theta \cos \theta \), \( \cos 2\theta = \cos^2 \theta - \sin^2 \theta \)
• Law of Sines: \( \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \)
• Law of Cosines: \( c^2 = a^2 + b^2 - 2ab \cos C \)
• Inverse Functions: \( \sin^{-1} x, \cos^{-1} x, \tan^{-1} x \)
• Unit Circle: Values of trig functions at special angles (e.g., \(0^\circ, 30^\circ, 45^\circ, 60^\circ, 90^\circ\))
• Basic Graphs: Period \(2\pi\) for sine and cosine, \( \pi \) for tangent

Quick Reference Table

Type	Formula	Description
Pythagorean	\( \sin^2 \theta + \cos^2 \theta = 1 \)	Fundamental identity
Angle Sum	\( \sin(a+b) = \sin a \cos b + \cos a \sin b \)	Sum of angles formula
Double Angle	\( \cos 2\theta = 1 - 2\sin^2 \theta \)	Expression for cosine double angle
Law of Sines	\( \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \)	Relates sides and angles in triangle
Law of Cosines	\( c^2 = a^2 + b^2 - 2 a b \cos C \)	Generalized Pythagoras

Advice

Trigonometry Quick Tips

• Basic Ratios: Memorize sine, cosine, and tangent ratios for key angles.
• Use Reciprocal Relations: For cosecant, secant, and cotangent calculations.
• Apply Identities: Pythagorean and angle sum/difference to simplify expressions.
• Triangle Laws: Use law of sines and cosines for solving any triangle.
• Practice Unit Circle: Recognize value patterns and signs in different quadrants.

Trigonometry Speed Quiz

Test your speed with 5 trigonometry questions! You have 30 seconds per question.