The Three Primary Trigonometric Comparisons

Introduction to the Three Primary Trigonometric Ratios

When ancient mathematicians studied triangles, they discovered useful patterns in the ratio of sides in right triangles. There are three primary trigonometric ratios that we will learn: sine ( $\sin$ ), cosine ( $\cos$ ), and tangent ( $\tan$ ).

Angle	Sine Value	Decimal Value
$0^\circ$	$0$	$0$
$30^\circ$	$\frac{1}{2}$	$0.5$
$45^\circ$	$\frac{\sqrt{2}}{2}$
$60^\circ$	$\frac{\sqrt{3}}{2}$
$90^\circ$	$1$	$1$

Angle	Cosine Value	Decimal Value
$0^\circ$	$1$	$1$
$30^\circ$	$\frac{\sqrt{3}}{2}$
$45^\circ$	$\frac{\sqrt{2}}{2}$
$60^\circ$	$\frac{1}{2}$	$0.5$
$90^\circ$	$0$	$0$

The Three Primary Trigonometric Comparisons

Introduction to the Three Primary Trigonometric Ratios

The Three Primary Trigonometric Comparisons

Introduction to the Three Primary Trigonometric Ratios

Understanding the Sides of a Right Triangle

Sine

Examples of Sine Values

Cosine

Examples of Cosine Values

Tangent

Examples of Tangent Values

Relationship between Sin, Cos, and Tan in the Unit Circle

Relationships Between the Three Trigonometric Ratios

Exercise

Check Your Answer

Angle	Tangent Value	Decimal Value
$0^\circ$	$0$	$0$
$30^\circ$	$\frac{1}{\sqrt{3}}$
$45^\circ$	$1$	$1$
$60^\circ$	$\sqrt{3}$
$90^\circ$	Undefined	Undefined