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

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