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

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 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 trigonometric ratios in context

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

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?

Checking and securing understanding of the unit circle

Lesson outcome