Trigonometry Fundamentals Flashcards

Vocabulary flashcards covering the fundamental concepts of Grade 10 Trigonometry, including similarity, ratios, reciprocals, reduction formulas, special triangles, and 2-D terminology.

Similar Triangles

Triangles where corresponding angles are equal and corresponding sides are in proportion.

Sine ($\sin \theta$)

The trigonometric ratio defined as $\frac{\text{Opposite}}{\text{Hypotenuse}}$.

Cosine ($\cos \theta$)

The trigonometric ratio defined as $\frac{\text{Adjacent}}{\text{Hypotenuse}}$.

Tangent ($\tan \theta$)

The trigonometric ratio defined as $\frac{\text{Opposite}}{\text{Adjacent}}$.

SOHCAHTOA

A mnemonic used to remember the definitions of the trigonometric ratios sine, cosine, and tangent.

Cosecant ($\text{cosec } \alpha$)

The reciprocal of the sine function, calculated as $\frac{1}{\sin \alpha}$.

Secant ($\text{sec } \alpha$)

The reciprocal of the cosine function, calculated as $\frac{1}{\cos \alpha}$.

Cotangent ($\text{cot } \alpha$)

The reciprocal of the tangent function, calculated as $\frac{1}{\tan \alpha}$.

CAST Diagram

A diagram marking which trigonometric functions are positive in each quadrant: All in Q1, Sine in Q2, Tangent in Q3, and Cosine in Q4.

Reduction: $\sin(180^\circ - \theta)$

A basic reduction formula that simplifies to $\sin \theta$.

Reduction: $\cos(180^\circ - \theta)$

A basic reduction formula that simplifies to $-\cos \theta$.

Reduction: $\sin(180^\circ + \theta)$

A basic reduction formula that simplifies to $-\sin \theta$.

$$\sin 60^\circ$$

A special triangle ratio equal to $\frac{\sqrt{3}}{2}$.

$$\cos 60^\circ$$

A special triangle ratio equal to $\frac{1}{2}$.

$$\tan 60^\circ$$

A special triangle ratio equal to $\sqrt{3}$.

$$\sin 30^\circ$$

A special triangle ratio equal to $\frac{1}{2}$.

$$\cos 30^\circ$$

A special triangle ratio equal to $\frac{\sqrt{3}}{2}$.

$$\tan 30^\circ$$

A special triangle ratio equal to $\frac{1}{\sqrt{3}}$.

$$\sin 45^\circ$$

A special triangle ratio equal to $\frac{1}{\sqrt{2}}$.

$$\tan 45^\circ$$

A special triangle ratio equal to $1$.

Angle of Elevation

The angle formed between a horizontal line and the line of sight when looking upward at an object.

Angle of Depression

The angle formed between a horizontal line and the line of sight when looking downward at an object.