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 trigonometric ratios

Maths

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

Non right-angled trigonometry

What trigonometric ratio would you use to work out the length $$k$$?

What trigonometric ratio would you use to work out the length $$b$$?

What trigonometric ratio would you use to work out the length $$e$$?

Work out the length $$b$$ to 1 decimal place.

Work out the length $$e$$ to 1 decimal place.

When $$a$$ = 6 cm and $$b$$ = 5 cm, angle $$x$$° is ...

When $$a$$ = 6 cm and $$c$$ = 12 cm, angle $$x$$° is ...

When $$b$$ = 4 cm and $$c$$ = 8 cm, angle $$x$$° is ...

When $$a$$ = 2 cm and $$b$$ = 1 cm, angle $$x$$° is ...

A right angled triangle is drawn and an angle $$x$$ is indicated. The opposite length to $$x$$ is labelled $$a$$, the adjacent length to $$x$$ is $$b$$ and the hypotenuse is $$c$$. 

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

What functions do we use to find a missing angle when provided with two sides in a right-angled triangle?

Which of the following calculations will calculate the answer to the length $$e$$?

$$\theta°=\arccos\left(\frac{\text{adj}}{\text{hyp}}\right)$$

$$\text{hyp}\times\cos(\theta°)=\text{adj}$$

$$\text{hyp}=\frac{\text{adj}}{\cos(\theta°)}$$

$$\cos(\theta°)=\frac{\text{hyp}}{\text{adj}}$$

Which of the following are equivalent to $$\cos(\theta°)=\frac{\text{adj}}{\text{hyp}}$$?

$$\text{adj}\times\tan(\theta°)=\text{opp}$$

$$\tan(\theta°)=\frac{\text{adj}}{\text{opp}}$$

$$\text{adj}=\frac{\text{opp}}{\tan(\theta°)}$$

$$\theta°=\arctan\left(\frac{\text{opp}}{\text{adj}}\right)$$

Which of the following are equivalent to $$\tan(\theta°)=\frac{\text{opp}}{\text{adj}}$$?

$$\text{hyp}=\frac{\sin(\theta°)}{\text{opp}}$$

$$\theta°=\arcsin\left(\frac{\text{opp}}{\text{hyp}}\right)$$

$$\text{hyp}=\frac{\text{opp}}{\sin(\theta°)}$$

$$\text{hyp}\times\sin(\theta°)=\text{opp}$$

Which of the following are equivalent to $$\sin(\theta°)=\frac{\text{opp}}{\text{hyp}}$$?

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

Checking and securing understanding of trigonometric ratios

Lesson outcome

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