New
New
Year 10
Foundation

Calculate trigonometric ratios for 30° and 60°

I can calculate trigonometric ratios for 30° and 60°.

New
New
Year 10
Foundation

Calculate trigonometric ratios for 30° and 60°

I can calculate trigonometric ratios for 30° and 60°.

Lesson details

Key learning points

  1. The trigonometric ratios for 30° and 60° can be calculated using an equilateral triangle
  2. The triangle should have lengths of 2 units
  3. By splitting the triangle into two right-angled triangles, you can calculate the ratios

Common misconception

Trigonometry always involves rounding.

Try evaluating sin(30) on your calculator. What answer do you get?

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.

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.
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.
Three trigonometric ratios are sine, cosine and .
Correct Answer: tangent
Q2.
Lucas has used his calculator to work out the value of $$\cos(48^\circ)$$. What is the value to 2 decimal places?
An image in a quiz
Correct Answer: 0.67
Q3.
Izzy has used her calculator to answer a trigonometry question. What is the length of the hypotenuse?
An image in a quiz
$$\sin(54)$$
2.427050983
Correct answer: 3
Q4.
Laura has used her calculator to answer a trigonometry question. What is the length of the adjacent?
An image in a quiz
Correct answer: 5
7.197782698
$$\cos(46)$$
Q5.
Andeep has attempted to use his calculator to answer a trigonometry question but has found himself with this message on his calculator. What might he have done wrong?
An image in a quiz
Correct answer: Used sine when he should have used tangent.
Used sine when he should have used cosine.
Forgotten to have his angle in the calculation.
Correct answer: Inputted the lengths for the opposite and hypotenuse the wrong way around.
Q6.
Which calculations are correct to find the length marked $$x$$?
An image in a quiz
Correct answer: $$x=\sqrt{9^2-8^2}$$
$$x=\frac{9}{\sin(63^\circ)}$$
$$x=\frac{9}{\cos(63^\circ)}$$
Correct answer: $$x=9\cos(63^\circ)$$
Correct answer: $$x=\frac{8}{\tan(63^\circ)}$$

6 Questions

Q1.
Which type of triangle can help deduce the exact trigonometric ratios for $$30^\circ$$ and $$60^\circ$$?
scalene triangle
isosceles triangle
Correct answer: equilateral triangle
Q2.
What is the exact value of $$\cos(30^\circ)$$?
An image in a quiz
$$\frac{1}{2}$$
Correct answer: $$\frac{\sqrt{3}}{2}$$
$$\frac{1}{\sqrt{3}}$$
$$\frac{2}{\sqrt{3}}$$
$$\sqrt{3}$$
Q3.
What is the exact value of $$\sin(60^\circ)$$?
An image in a quiz
$$\frac{1}{2}$$
Correct answer: $$\frac{\sqrt{3}}{2}$$
$$\frac{1}{\sqrt{3}}$$
$$\frac{2}{\sqrt{3}}$$
$$\sqrt{3}$$
Q4.
What is the exact value of $$\tan(60^\circ)$$?
An image in a quiz
$$\frac{1}{2}$$
$$\frac{\sqrt{3}}{2}$$
$$\frac{1}{\sqrt{3}}$$
$$\frac{2}{\sqrt{3}}$$
Correct answer: $$\sqrt{3}$$
Q5.
What is the exact value of $$\cos(60^\circ)+\sin(30^\circ)$$?
Correct Answer: 1
Q6.
What is the exact value of $$\sin(60^\circ)\times\tan(30^\circ)$$?
Correct Answer: 0.5, half, 1/2