- Year 11
Drawing the tangent graph
I can draw the graph for the tangent trigonometric function.
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.
Keywords
Period (of a function) - For a repeating function, the period is the distance of one repetition of the entire function.
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.
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.How many times does a tangent intersect a circle?
Q2.What is the name of this function?
Q3.What is the name of this function?
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?
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?
Q6.Match the equivalent values.
$$\sin(30°)$$ - $$\frac{4.5}{9}$$
$$\cos(0°)$$ - $$\frac{12}{12}$$
$$\sin(45°)$$ - $$\frac{3}{3\sqrt{2}}$$
$$\sin(0°)$$ - $$\frac{0}{12}$$
Assessment exit quiz
6 Questions
Q1.Match the equivalent values.
$$\tan(0°)$$ - 0
$$\tan(30°)$$ - $$\frac{\sqrt{3}}{3}$$
$$\tan(45°)$$ - 1
$$\tan(60°)$$ - $$\sqrt{3}$$
$$\tan(90°)$$ - Undefined
Q2.Which trigonometric function is shown?
Q3.What other types of graphs have undefined values?
Q4.What do the sine and cosine graphs look like?
Q5.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.
Q6.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.
