New
New
Year 11
Higher

Drawing the tangent graph

I can draw the graph for the tangent trigonometric function.

New
New
Year 11
Higher

Drawing the tangent graph

I can draw the graph for the tangent trigonometric function.

Lesson details

Key learning points

  1. The unit circle can help you predict what the tangent graph will look like
  2. The tangent graph has asymptotes
  3. 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.

If you wish, ask pupils to create the table of values through deriving the exact values for each stated value of θ.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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6 Questions

Q1.
How many times does a tangent intersect a circle?
Correct Answer: 1, one, once
Q2.
What is the name of this function?
An image in a quiz
$$y=\cos(\theta°)$$
Correct answer: $$y=\sin(\theta°)$$
$$y=x^2$$
$$y=x^3$$
Q3.
What is the name of this function?
An image in a quiz
Correct answer: $$y=\cos(\theta°)$$
$$y=\sin(\theta°)$$
$$y=x^2$$
$$y=x^3$$
Q4.
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?
Correct Answer: 4, four
Q5.
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?
Correct Answer: 5, five
Q6.
Match the equivalent values.
Correct Answer:$$\sin(30°)$$,$$\frac{4.5}{9}$$

$$\frac{4.5}{9}$$

Correct Answer:$$\cos(0°)$$,$$\frac{12}{12}$$

$$\frac{12}{12}$$

Correct Answer:$$\sin(45°)$$,$$\frac{3}{3\sqrt{2}}$$

$$\frac{3}{3\sqrt{2}}$$

Correct Answer:$$\sin(0°)$$,$$\frac{0}{12}$$

$$\frac{0}{12}$$

6 Questions

Q1.
Match the equivalent values.
Correct Answer:$$\tan(0°)$$,0

0

Correct Answer:$$\tan(30°)$$,$$\frac{\sqrt{3}}{3}$$

$$\frac{\sqrt{3}}{3}$$

Correct Answer:$$\tan(45°)$$,1

1

Correct Answer:$$\tan(60°)$$,$$\sqrt{3}$$

$$\sqrt{3}$$

Correct Answer:$$\tan(90°)$$,Undefined

Undefined

Q2.
Which trigonometric function is shown?
An image in a quiz
$$y=\sin(\theta°)$$
$$y=\cos(\theta°)$$
Correct answer: $$y=\tan(\theta°)$$
$$y=x^2$$
$$y=x^3$$
Q3.
What other types of graphs have undefined values?
Correct answer: Reciprocal graphs
Cubic graphs
Quadratic graphs
Linear graphs
Q4.
What do the sine and cosine graphs look like?
They increase upwards rapidly and have asymptotes so have undefined values.
Correct answer: The look like a wave with a maximum of 1 and minimum of -1.
Correct answer: A period is seen using $$ 0°\leq x \leq 360° $$.
Q5.
Using the interval, $$ 0°\leq x \leq 360° $$, match the local maximum coordinates with the trigonometric graph.
Correct Answer:$$y=\sin(\theta°)$$,(90°, 1)

(90°, 1)

Correct Answer:$$y=\cos(\theta°)$$,(0°, 1) and (360°, 1)

(0°, 1) and (360°, 1)

Correct Answer:$$y=\tan(\theta°)$$,There are no local maximums.

There are no local maximums.

Q6.
Using the interval, $$ 0°\leq x \leq 360° $$, match the local minimum coordinates with the trigonometric graph.
Correct Answer:$$y=\sin(\theta°)$$,(270°, -1)

(270°, -1)

Correct Answer:$$y=\cos(\theta°)$$,(180°, -1)

(180°, -1)

Correct Answer:$$y=\tan(\theta°)$$,There are no local minimums.

There are no local minimums.