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

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

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.

Using the 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

Tangent ratio

Using the sine ratio

Using the cosine 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

Using triangle ABC, if θ = 38ᵒ and BC = 14 cm, what is the length of the adjacent side AC to 1 d.p. ?

What value of $$y$$ will produce the same result for tan($$y$$) and cos(90ᵒ)?

Using triangle ABC, if θ = 18ᵒ and BC = 10 cm, what is the length of the adjacent side AC to 1 d.p. ?

What value of $$y$$ will produce the same result for tan($$y$$) and cos(0ᵒ)?

Using triangle ABC, if θ =26ᵒ and AC = 10 cm, what is the length of BC to 1 d.p. ?

Using triangle ABC, if θ =35ᵒ and AC = 10 cm, what is the length of BC to 1 d.p. ?

In a right triangle, if the hypotenuse is 25 cm and a second side is 20 cm, what is the perimeter? (Use a calculator to help you.)

In a right triangle, if the hypotenuse is 125 cm and a second side is 100 cm, what is the area? (Use a calculator to help you.)

What is the value of cos(37ᵒ) to 2 d.p. ?

Which of these is a correct formula for using the Cosine function?

Which of these is a correct formula for using the Sine function?

Which of these is a correct formula for using the Tangent function?

Using the tangent ratio

Lesson outcome