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

Drawing the sine and cosine graphs

Drawing the tangent graph

Interpreting the trigonometric graphs

The area of any triangle

Calculating the area of any triangle when the height is not known

The sine rule

The cosine rule

Using the sine and cosine rules

Considering the appropriate trigonometric rule

Problem solving with non right-angled trigonometry

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.

In this unit, pupils explore how to apply knowledge in trigonometry to non right-angled triangles.

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

Starter Quiz

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