Drawing the tangent graph | Maths | Quizalize & Oak National Academy

Starter quiz

How many times does a tangent intersect a circle?

'1' ✓
What is the name of this function?

$y=\cos(\theta°)$

$y=\sin(\theta°)$ ✓

$y=x^2$

$y=x^3$
What is the name of this function?

$y=\cos(\theta°)$ ✓

$y=\sin(\theta°)$

$y=x^2$

$y=x^3$
Using Desmos and an $x$ axis interval of $0°\leq x\leq 720°$ , how many times does the cosine graph pass through the $x$ axis?

'4' ✓
Using Desmos and an $x$ axis interval of $0°\leq x\leq 720°$ , how many times does the sine graph pass through the $x$ axis?

'5' ✓
Match the equivalent values.

$\sin(30°)$

⇔

$\frac{4.5}{9}$ ✓

$\cos(0°)$

⇔

$\frac{12}{12}$ ✓

$\sin(45°)$

⇔

$\frac{3}{3\sqrt{2}}$ ✓

$\sin(0°)$

⇔

$\frac{0}{12}$ ✓

Exit quiz

Match the equivalent values.

$\tan(0°)$

⇔

0 ✓

$\tan(30°)$

⇔

$\frac{\sqrt{3}}{3}$ ✓

$\tan(45°)$

⇔

1 ✓

$\tan(60°)$

⇔

$\sqrt{3}$ ✓

$\tan(90°)$

⇔

Undefined ✓
Which trigonometric function is shown?

$y=\sin(\theta°)$

$y=\cos(\theta°)$

$y=\tan(\theta°)$ ✓

$y=x^2$

$y=x^3$
What other types of graphs have undefined values?

Reciprocal graphs ✓

Cubic graphs

Quadratic graphs

Linear graphs
What do the sine and cosine graphs look like?

They increase upwards rapidly and have asymptotes so have undefined values.

The look like a wave with a maximum of 1 and minimum of -1. ✓

A period is seen using $0°\leq x \leq 360°$ . ✓
Using the interval, $0°\leq x \leq 360°$ , match the local maximum coordinates with the trigonometric graph.

$y=\sin(\theta°)$

⇔

(90°, 1) ✓

$y=\cos(\theta°)$

⇔

(0°, 1) and (360°, 1) ✓

$y=\tan(\theta°)$

⇔

There are no local maximums. ✓
Using the interval, $0°\leq x \leq 360°$ , match the local minimum coordinates with the trigonometric graph.

$y=\sin(\theta°)$

⇔

(270°, -1) ✓

$y=\cos(\theta°)$

⇔

(180°, -1) ✓

$y=\tan(\theta°)$

⇔

There are no local minimums. ✓

Worksheet

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Presentation

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Video

Lesson Details

Key learning points

The unit circle can help you predict what the tangent graph will look like
The tangent graph has asymptotes
The trigonometric functions have different periods.

Common misconception

Pupils may have their calculator set to radians instead of degrees.

The first check for understanding is designed to catch this but it is worth checking that the correct unit of measurement is being used throughout the lesson.

Keywords

Period (of a function) - For a repeating function, the period is the distance of one repetition of the entire function.