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6.3 Trigonometric Functions of Angles

Focus on trigonometry from a point and tangent from coordinates.

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01Reference anglesWorked steps · five questions 02Exact trig values of any angleWorked steps · five questions 03Finding values from one ratio and a quadrantWorked steps · five questions 04Area of a triangle using sineWorked steps · five questions

Lesson brief and rules

6.3 Trigonometric Functions of Angles

At $(x,y)$ with $r=\sqrt{x^{2}+y^{2}}, \sin \theta =\frac{y}{r}$ and $\cos \theta =\frac{x}{r}$ .

Worked example

1

01 / A terminal point is

(12,16)

. Find

\cos \theta

02 /

r=\sqrt{(12)^{2}+(16)^{2}}=20

;

\dfrac{x}{r}=\dfrac{3}{5}

03 / Answer:

\dfrac{3}{5}

Worked example 2 · Tangent from coordinates

A terminal point is $(4,6)$ . Find $\tan \theta$ .

$\tan \theta =\dfrac{y}{x}=\dfrac{6}{4}$ . Answer: $\dfrac{6}{4}$

15 questions covering every idea, with a worked answer for each.Start practice ↗

Textbook reference: Stewart, Redlin & Watson, Precalculus: Mathematics for Calculus, 7th ed. (Cengage, 2016). The explanations and practice here are original, organized by textbook section.

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6.3 Trigonometric Functions of Angles

Ideas in this lesson

6.3 Trigonometric Functions of Angles