Skip to content
Oak National Academy
Oak National Academy
View my library
0
Teachers
Pupils
View unit
New
New
Lesson 2 of 11

    Drawing the sine and cosine graphs

    I can draw the graphs for the trigonometric functions sine and cosine.

    Download all
    View unit
    Lesson 2 of 11
    New
    New

      Drawing the sine and cosine graphs

      I can draw the graphs for the trigonometric functions sine and cosine.

      Download all

      These resources will be removed by end of Summer Term 2025.

      Switch to our new teaching resources now - designed by teachers and leading subject experts, and tested in classrooms.

      These resources were created for remote use during the pandemic and are not designed for classroom teaching.

      View new resources

      Lesson details

      Key learning points

      1. The unit circle can help you predict what the graphs of the trigonometric functions will look like
      2. The sine and cosine graphs have y values between −1 and 1

      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.

      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.

      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 (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

      Lesson video

      Skip lesson video

      Loading...

      Prior knowledge starter quiz

      Download quiz pdf

      6 Questions

      Q1.
      Match the trigonometric ratio with the correct definition.

      Correct Answer:The sine of an angle is the ,$$y$$-coordinate (P) on the triangle formed inside the unit circle.

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

      Correct Answer:The cosine of an angle is the ,$$x$$-coordinate (P) on the triangle formed inside the unit circle.

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

      Correct Answer:The tangent is the ,line that intersects the circle exactly once.

      line that intersects the circle exactly once.

      Q2.
      Match the following values.

      Correct Answer:0,$$\sin(0°)$$

      $$\sin(0°)$$

      Correct Answer:0.5,$$\sin(30°)$$

      $$\sin(30°)$$

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

      $$\sin(45°)$$

      Correct Answer:$$\frac{\sqrt{3}}{2}$$,$$\sin(60°)$$

      $$\sin(60°)$$

      Correct Answer:1,$$\sin(90°)$$

      $$\sin(90°)$$

      Correct Answer:0.985 (3 s.f),$$\sin(100°)$$

      $$\sin(100°)$$

      Q3.
      Match the following values.

      Correct Answer:1,$$\cos(0°)$$

      $$\cos(0°)$$

      Correct Answer:$$\frac{\sqrt{3}}{2}$$,$$\cos(30°)$$

      $$\cos(30°)$$

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

      $$\cos(45°)$$

      Correct Answer:0.5,$$\cos(60°)$$

      $$\cos(60°)$$

      Correct Answer:0,$$\cos(90°)$$

      $$\cos(90°)$$

      Correct Answer:-0.174 (3 s.f),$$\cos(100°)$$

      $$\cos(100°)$$

      Q4.
      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.

      Correct Answer: 56.3°, 56.3 degrees, 56.3

      Q5.
      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 $$x$$°.

      Correct Answer: 30°, 30, 30 degrees

      Q6.
      Jun draws a square with lengths 7 cm. What is the angle between the diagonals and the length 7 cm?

      Correct Answer: 45°, 45, 45 degrees

      Assessment exit quiz

      Download quiz pdf

      6 Questions

      Q1.
      The __________ allows us to work out values for $$\sin(\theta°)$$ and $$\cos(\theta°)$$.

      unit graph
      Correct answer: unit circle
      unitary method
      unit square

      Q2.
      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?

      An image in a quiz
      Correct answer: Go to settings and change from radians to degrees.
      Correct answer: 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.

      Q3.
      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°?

      An image in a quiz
      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 $$ -1\leq x\leq 1$$.
      Correct answer: Go to settings and change the $$y$$ axis interval to $$ -1\leq y\leq 1$$.

      Q4.
      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?

      Correct Answer: 3, three

      Q5.
      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?

      Correct Answer: 2, two

      Q6.
      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 $$y = \cos(x°)$$?

      Correct answer: 45°
      Correct answer: 225°
      90°
      180°
      135°

      Lesson appears in

      UnitMaths / Non right-angled trigonometry

      Maths

      Show Higher unit