CLEP Precalculus-Core Concept Cheat Sheet - 09 Basic Trigonometry - Key Ratios & Identities

Oct 13, 2026

CLEP Precalculus basic trigonometry study sheet focused on core definitions, reference angles, right triangles, and the unit circle. Summarizes the six trigonometric functions as right-triangle side ratios and highlights SOHCAHTOA for primary relationships. Includes sign rules by quadrant, common special angles (30°, 45°, 60°), and a compact set of reciprocal, quotient, Pythagorean, and cofunction identities. Ends with the Pythagorean theorem for right triangles.

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09: Basic Trigonometry

Key Terms and Trigonometric Function Ratios

Signs by Quadrant

Common Trigonometry Angles

Trigonometric Identities

Pythagorean Theorem

Cofunction Identities

How to Use This Cheat Sheet

CLEP Precalculus-Core Concept Cheat Sheet | 09: Basic Trigonometry | | | | | | | --- | --- | --- | --- | --- | --- | | Key Terms | | Trigonometric Function Ratios | | | | | • Domain: the set of possible values of θ ; input.
• Fundamental period: the smallest interval over which a periodic function repeats itself.
• Period: any interval over which a function repeats itself.
• Periodic function: a function that repeats itself at regular intervals.
• Quadrant: one of four sections the coordinate plane is divided into by its axes.
• Range: the set of possible values of f(θ); output.
• Reference angle: given angle θ, the acute angle between the terminal side of θ and the x-axis.
• Right triangle: a geometric figure having three sides and three angles with exactly one angle with a measure of 90° .
• Trigonometric identity: a relation between two or more trigonometric functions .
• Unit circle: a circle of radius one centered at the origin. | | The six trigonometric functions can be defined as ratios of the lengths of the sides of a right triangle.

Use “SOHCAHTOA” to remember the primary ratios . | | | | | Signs of Trigonometric Functions | | | | | | | The quadrant a standard angle lies in tells the sign of the trigonometric function values.

Use the first letters of “All Students Take Calculus” to remember:
• All trigonometric functions are positive in Quadrant I.
• Sine (and cosecant) are positive in Quadrant II.
• Tangent (and cotangent) are positive in Quadrant III.
• Cosine (and secant) are positive in Quadrant IV. | | | | | | | | | Common Angles of Trigonometry | | | | | | | √3 | | | 1 | | | | Angle θ sin θ cos θ tan θ 30° (or π/6) 1/2 √3/2 √3/3 45° (or π/4) √2/2 √2/2 1 65° (or π/3) √3/2 1/2 √3 | | | | | | | Trigonometric Identities | | | | | | | • Reciprocal Identities
sin θ = cs~~θ ~~ cos θ = se~~θ ~~ tan θ = c1o~~t θ~~
csc θ = ~~si~~~~θ ~~ sec θ = s~~ θ ~~ cot θ = ~~ta~~~~θ~~• Quotient Identities
tan θ = scoi~~ ~~nsθ~~θ ~~ AND cot θ = cso~~i~~snθ~~θ~~
• Pythagorean Identities
sin2 θ + cos2 θ = 1 1 + tan2 θ = sec2 θ
1 + cot 2 θ = csc2 θ | | | | | Pythagorean Theorem | | | | | | | The Pythagorean theorem states that the square of the length of the hypotenuse, r, is equal to the sum of the squares of the lengths of the two legs of a right triangle, a and b.
r2 = a2 + b2 | | | | | | | | a | | | | | | | | • Cofunction Identities
sin(90 − θ) = cos θ cos(90° − θ) = sin θ tan(90° − θ) = cot θ | | csc(90° − θ) = sec θ sec(90° − θ) = csc θ cot(90° − θ) = tan θ | | How to Use This Cheat Sheet: These are the key concepts related this topic. Try to read through it carefully twice then write it out on a blank sheet of paper. Review it again before the exam .

FAQs

What is the reference angle and how is it used?

The reference angle is the acute angle formed between the terminal side of θ and the x-axis. It helps determine which triangle relationships apply when evaluating trig values.

How do you remember the primary trigonometric ratios?

Use SOHCAHTOA: sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, and tangent is opposite over adjacent. The sheet summarizes these as right-triangle side ratios.

Which trigonometric identities are included on this cheat sheet?

It includes reciprocal identities (e.g., sin θ and csc θ), quotient identities (relationships between tan, cot, and sine/cosine), Pythagorean identities (sin² θ + cos² θ = 1 and related forms), and cofunction identities like sin(90 − θ) = cos θ.

Oct 13, 2026

Upload by River Wang