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.

Checking and securing understanding of the unit circle

Maths

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.

Right-angled trigonometry

What are the features of the unit circle?

The sine of an angle is the __________ of the point where the radius of the unit circle has been rotated through that angle.

The __________ of an angle is the $$x$$-coordinate of the point where the radius of the unit circle has been rotated through that angle.

The tangent of an angle is the __________ of the point where the line (the triangle’s hypotenuse) intersects the tangent line. 

Match up the correct trigonometric values.

$$\sin(\theta^\circ)=\cos(\theta^\circ)$$

$$\sin(\theta^\circ)+\cos(\theta^\circ)=1$$

$$(\sin(\theta^\circ))^2+(\cos(\theta^\circ))^2=1$$

A tangent to a curve at a given point is a line that intersects the curve at that point. Both the tangent and the curve have the same {{}} at the given point.

A right-angled triangle has a hypotenuse of 1 cm and a short side of 0.6 cm, what is the length of the third side of the triangle?

A right-angled triangle has a hypotenuse of 1 cm and a short side of 0.54 cm, what is the length of the third side of the triangle, to 2 decimal places?

A right-angled triangle has a hypotenuse of 2.6 cm and a short side of 1 cm, what is the length of the third side of the triangle?

This lesson will be removed by end of Summer Term 2025.

Checking and securing understanding of the unit circle

Lesson outcome

This lesson will be removed by end of Summer Term 2025.