The adjacent side of a right-angled triangle is the side which is next to both the right angle and the marked angle.

The opposite side of a right-angled triangle is the side which is opposite the marked angle.

The trigonometric ratios are ratios between each pair of lengths in a right-angled triangle.

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

Tangent ratio

Maths

Checking and securing understanding of similar triangles

Checking and securing understanding of Pythagoras' theorem

The unit circle

Scaling the right-angled triangle from the unit circle

Sine and cosine ratios

Using the sine ratio

Using the cosine ratio

Using the tangent ratio

Choosing the right trigonometric ratio

Choosing an appropriate method for finding lengths of a triangle

Problem solving with trigonometry

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

In the prior unit, pupils continued to build on their understanding of congruence and similarity with right-angled triangles. In this unit, similarity is used to extend a right-angled triangle in the unit circle to any other right-angled triangle.

In this unit pupils learn how to recognise the relationship between the unit circle and the trigonometric ratios of sine, cosine and tangent. Pupils then apply this knowledge to solve trigonometric problems.

Trigonometry

Match the estimated values with the trigonometric functions below.

For which value of θ is tan (θ) undefined?

In a right triangle, if you are provided with θ and the opposite side, which function would you use to find the adjacent side? 

Which of these is a rearrangement of $$tan(θ)=\frac{opp}{adj}$$

Which of these is not an rearrangement of $$tan(θ)=\frac{opp}{adj}$$

For a right triangle ABC, if angle CBA = 33ᵒ, and the adjacent side to that angle is 1 cm, what is the length of the side opposite angle CBA? 

In a right triangle, if the hypotenuse is 32.5 cm and a second side is 12.5 cm, what is the perimeter? (Use a calculator to help you.)

What is the value of θ for sin(θ) = tan(θ) ?

In a right triangle, if the hypotenuse is 32.5 cm and a second side is 12.5 cm, what is the area? (Use a calculator to help you.)

What is the value of θ for sin(θ) = cos(θ) ?

Tangent ratio

Lesson outcome