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Year 10
Foundation

Calculate trigonometric ratios for 0°, 45° and 90°

I can calculate trigonometric ratios for 0°, 45° and 90°.

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New
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Year 10
Foundation

Calculate trigonometric ratios for 0°, 45° and 90°

I can calculate trigonometric ratios for 0°, 45° and 90°.

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

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Lesson details

Key learning points

  1. The trigonometric ratios for 45° can be calculated using a square
  2. The square should have lengths of 1 unit
  3. By splitting the square into two right-angled triangles, you can calculate the ratio
  4. The ratios for 0° and 90° can be reasoned

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.

  • Tangent function - The tangent of an angle (tan(θ°)) is the y-coordinate of point Q on the triangle which extends from the unit circle.

Common misconception

Trigonometry always involves rounding.

Try evaluating sin(0) on your calculator. What answer do you get?


To help you plan your year 10 maths lesson on: Calculate trigonometric ratios for 0°, 45° and 90°, download all teaching resources for free and adapt to suit your pupils' needs...

The first learning cycle is heavily scaffolded to support pupils who may find this difficult. You may wish to remove some of this so your pupils can do more deduction.
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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

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Starter quiz

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6 Questions

Q1.
Which trigonometric ratio is between the opposite and adjacent?
sine
cosine
Correct answer: tangent
Q2.
Which of these have a value of $$\frac{\sqrt{3}}{2}$$?
An image in a quiz
$$\sin(30^\circ)$$
Correct answer: $$\cos(30^\circ)$$
$$\tan(30^\circ)$$
Correct answer: $$\sin(60^\circ)$$
$$\cos(60^\circ)$$
Q3.
$$\tan(60^\circ)=\sqrt{3}$$, so what is $$(\tan(60^\circ))^2$$?
Correct Answer: 3, three
Q4.
Sam has used their calculator to answer a trigonometry question. What is the answer a value of?
An image in a quiz
opposite
adjacent
Correct answer: hypotenuse
angle
Q5.
Aisha has used their calculator to answer a trigonometry question. What is the answer a value of?
An image in a quiz
Correct answer: opposite
adjacent
hypotenuse
angle
Q6.
Order the stages of working for $$\sin(\theta)\div\cos(\theta)$$.
1 - $$\sin(\theta)=\frac{\text{opp}}{\text{hyp}}$$
2 - and $$\cos(\theta)=\frac{\text{adj}}{\text{hyp}}$$
3 - Hence, $$\sin(\theta)\div\cos(\theta)$$
4 - $$=\frac{\text{opp}}{\text{hyp}}\div\frac{\text{adj}}{\text{hyp}}$$
5 - $$=\frac{\text{opp}}{\text{hyp}}\times\frac{\text{hyp}}{\text{adj}}$$
6 - $$=\frac{\text{opp}}{\text{adj}}$$
7 - $$=\tan(\theta)$$.

Exit quiz

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6 Questions

Q1.
A right-angled isosceles triangle has...
Correct answer: ... two $$45^\circ$$ angles and a right-angle.
... three different edge lengths.
Correct answer: ... a hypotenuse $$\sqrt{2}$$ times longer than the other two edges.
... two right-angles and one other angle.
Q2.
What is the exact value of $$\cos(45^\circ)$$?
An image in a quiz
Correct answer: $$\frac{1}{\sqrt{2}}$$
$$1$$
$$\sqrt{2}$$
Correct answer: $$\frac{\sqrt{2}}{2}$$
Q3.
What is the exact value of $$\tan(45^\circ)$$?
An image in a quiz
$$\frac{1}{\sqrt{2}}$$
Correct answer: $$1$$
$$\sqrt{2}$$
$$\frac{\sqrt{2}}{2}$$
Q4.
What does this diagram show?
An image in a quiz
$$\sin(0^\circ)=1$$
Correct answer: $$\sin(0^\circ)=0$$
$$\cos(0^\circ)=0$$
Correct answer: $$\cos(0^\circ)=1$$
Correct answer: $$\tan(0^\circ)=0$$
Q5.
This diagram shows that $$\sin(90^\circ)=1$$ and $$\cos(90^\circ)=0$$, but what is $$\tan(90^\circ)$$?
An image in a quiz
0 as there is not an answer.
Correct answer: undefined as the line does not intersect the tangent.
1 as the tangent is $$x=1$$
Q6.
What is the exact value of $$\tan(45^\circ)+\sin(90^\circ)$$?
Correct Answer: 2, two