Drawing the sine and cosine graphs | Maths | Quizalize & Oak National Academy

Starter quiz

Match the trigonometric ratio with the correct definition.

The sine of an angle is the

⇔

$y$ -coordinate (P) on the triangle formed inside the unit circle. ✓

The cosine of an angle is the

⇔

$x$ -coordinate (P) on the triangle formed inside the unit circle. ✓

The tangent is the

⇔

line that intersects the circle exactly once. ✓
Match the following values.

0

⇔

$\sin(0°)$ ✓

0.5

⇔

$\sin(30°)$ ✓

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

⇔

$\sin(45°)$ ✓

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

⇔

$\sin(60°)$ ✓

1

⇔

$\sin(90°)$ ✓

0.985 (3 s.f)

⇔

$\sin(100°)$ ✓
Match the following values.

1

⇔

$\cos(0°)$ ✓

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

⇔

$\cos(30°)$ ✓

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

⇔

$\cos(45°)$ ✓

0.5

⇔

$\cos(60°)$ ✓

0

⇔

$\cos(90°)$ ✓

-0.174 (3 s.f)

⇔

$\cos(100°)$ ✓
A right-angled triangle is drawn and an angle $x$ is indicated. The opposite length is 3 cm and the adjacent length is 2 cm. Work out the angle $x$ °. Give your answer to 1 decimal place.

'56.3°' ✓
A right-angled triangle is drawn and an angle $x$ is indicated. The opposite length is 8 cm and the hypotenuse length is 16 cm. Work out the angle $x$ °.

'30°' ✓
Jun draws a square with lengths 7 cm. What is the angle between the diagonals and the length 7 cm?

'45°' ✓

Exit quiz

The __________ allows us to work out values for $\sin(\theta°)$ and $\cos(\theta°)$ .

unit graph

unit circle ✓

unitary method

unit square
Andeep wants a sine graph from 0° to 360°. He opened Desmos and typed in "y=sin(x)". This image appears. What does Andeep need to do to see the sine graph between 0° and 360° degrees?

Go to settings and change from radians to degrees. ✓

Go to settings and change the $x$ axis interval to $0°\leq x\leq 360°$ . ✓

Go to settings and change the $y$ axis interval to $0°\leq y\leq 360°$ .

He should have typed in y = $x$ sin.
Andeep wants a sine graph from 0° to 360°. He opened Desmos and typed in "y=sin(x)". This image appears. What does Andeep need to do to see the full sine graph between 0° and 360°?

Go to settings and change the $x$ axis interval to $0°\leq x\leq 360°$ .

Go to settings and change the $y$ axis interval to $0°\leq y\leq 360°$ .

Go to settings and change the $x$ axis interval to $-1\leq x\leq 1$ .

Go to settings and change the $y$ axis interval to $-1\leq y\leq 1$ . ✓
Using Desmos and an $x$ axis interval of $0°\leq x\leq 360°$ , how many times does the sine graph pass through the $x$ axis?

'3' ✓
Using Desmos and an $x$ axis interval of $0°\leq x\leq 360°$ , how many times does the cosine graph pass through the $x$ axis?

'2' ✓
Using Desmos and an $x$ axis interval of $0°\leq x\leq 360°$ , what are the $x$ coordinates of the intersections of $y = \sin(x°)$ and $y = \cos(x°)$ ?

45° ✓

225° ✓

90°

180°

135°

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 graphs of the trigonometric functions will look like
The sine and cosine graphs have y values between −1 and 1

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

Trigonometric functions - Trigonometric functions are commonly defined as ratios of two sides of a right-angled triangle for a given angle.
Sine function - The sine of an angle (sin(θ°)) is the y-coordinate of point P on the triangle formed inside the unit circle.
Cosine function - The cosine of an angle (cos(θ°)) is the x-coordinate of point P on the triangle formed inside the unit circle.