Trigonometric functions are commonly defined as ratios of two sides of a right-angled triangle for a given angle.

The sine of an angle (sin(θ°)) is the y-coordinate of point P on the triangle formed inside the unit circle.

The cosine of an angle (cos(θ°)) is the x-coordinate of point P on the triangle formed inside the unit circle.

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

Applying trigonometric ratios in context

Maths

Checking and further securing understanding of Pythagoras' theorem

Using Pythagoras' theorem to justify a right-angled triangle

Calculating the length of a line segment

Checking and securing understanding of the unit circle

Checking and securing understanding of sine ratio problems

Checking and securing understanding of cosine problems

Checking and securing understanding of tangent ratio problems

Calculate trigonometric ratios for 30° and 60°

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

Applying Pythagoras' theorem in 3D

Applying trigonometric ratios in 3D

Advanced problem solving with right-angled trigonometry

In this unit, pupils have explored the trigonometric ratios for right-angled triangles in a variety of situations. In the future unit, pupils explore what can be done when we have a triangle that is not right-angled.

In the prior unit, pupils were introduced to the trigonometric ratios and developed the skills to ascertain which ratio would be appropriate for a given problem. In this unit, pupils are introduced to a variety of situations where this knowledge is required, such as 3-D problems and elevation/depression.

In this unit, pupils are introduced to a variety of situations where trigonometric ratios are required, such as 3-D problems and problems of elevation or depression.

Right-angled trigonometry

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?

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?

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?

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?

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.

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

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

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

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

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

Starter Quiz

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