Encourage pupils to draw the right-angled triangle for the scenario if they are unsure so that they can label the sides and be confident about which trigonometric function is needed.

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.

Pupils may be interested in further exploring how trigonometry can be useful in the real-world. Consider asking pupils to calculate the heights of various buildings using trigonometry.

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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Starter quiz

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6 Questions

Q1.

Which of the trigonometric ratios should you use to calculate $$x$$?

sine

Correct answer: cosine

tangent

Q2.

Which of the trigonometric ratios should you use to calculate $$x$$?

Correct answer: sine

cosine

tangent

Q3.

Work out the length of $$x$$, to 1 decimal place.

Correct Answer: 10.2 cm, 10.2

Q4.

Work out the length of $$x$$, to 1 decimal place.

Correct Answer: 6.9 cm, 6.9

Q5.

Work out the size of $$x$$, to the nearest degree.

Correct Answer: 55, 55 degrees

Q6.

Which of these calculations will find the value of $$x$$?

$$x=8\tan(41^\circ)$$

Correct answer: $$x=\frac{8}{\tan(41^\circ)}$$

Correct answer: $$x=8\tan(49^\circ)$$

$$x=\frac{8}{\tan(49^\circ)}$$

Exit quiz

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6 Questions

Q1.

A helicopter flies so that it is 6 miles due East and 2 miles due North of where it started. Which calculation finds the angle, $$x$$ to fly direct?

$$x=\tan\left(\frac{2}{6}\right)$$

$$x=\tan\left(\frac{6}{2}\right)$$

Correct answer: $$x=\arctan\left(\frac{2}{6}\right)$$

$$x=\arctan\left(\frac{6}{2}\right)$$

Q2.

A helicopter flies so that it is 2 miles due East and 6 miles due South of where it started. What is the angle, $$x$$, to the nearest degree to fly direct?

Correct Answer: 72

Q3.

A helicopter flies on an angle of $$38^\circ$$ direct to its destination, such that it is 4 miles due East of the start position. How far is the direct distance, to the nearest mile?

Correct Answer: 5, five, 5 miles

Q4.

A helicopter flies on an angle of $$38^\circ$$ direct to its destination, such that it is 4 miles due East of the start position. How far North of the start is it, to the nearest mile?

Correct Answer: 3, 3 miles, three

Q5.

A search and rescue helicopter spots a person out at sea. Using the diagram, work out the height of the helicopter above the sea level, to the nearest metre.

Correct Answer: 1834 m, 1834

Q6.

Using the diagram (not to scale), work out the height of the tree, to 1 decimal place.

Correct Answer: 11.6 m, 11.6