Checking and securing understanding of trigonometric ratios
I can appreciate the range of values of the trigonometric functions.
- Year 11
Checking and securing understanding of trigonometric ratios
I can appreciate the range of values of the trigonometric functions.
Lesson details
Key learning points
- The unit circle is a circle with a radius of one
- The unit circle is centered on the origin
- The sine of an angle is the y-coordinate of the point where the radius has been rotated through that angle
- The cosine of an angle is the x-coordinate of the point where the radius has been rotated through that angle
- The tangent of an angle is the length of the side opposite the angle along the tangent at x = 1 to the unit circle
Keywords
Trigonometric functions - Trigonometric functions are commonly defined as ratios of two sides of a right-angled triangle for a given angle.
Sine function - The sine of an angle (sin(θ°)) is the y-coordinate of point P on the triangle formed inside the unit circle.
Cosine function - The cosine of an angle (cos(θ°)) is the x-coordinate of point P on the triangle formed inside the unit circle.
Tangent function - The tangent of an angle (tan(θ°)) is the y-coordinate of point Q on the triangle which extends from the unit circle.
Common misconception
Pupils may use the incorrect trigonometric formula.
Encourage pupils to label their triangles with the name for each side. This helps to identify the opposite, adjacent and hypotenuse.
Licence
Prior knowledge starter quiz
6 Questions
Q1.Trigonometric functions are commonly defined as ratios of two sides of a right-angled triangle for a given angle. Select the trigonometric functions.
Q2.What functions do we use to find a missing angle when provided with two sides in a right-angled triangle?
Q3.Which of the following calculations will calculate the answer to the length $$e$$?

Q4.Which of the following are equivalent to $$\cos(\theta°)=\frac{\text{adj}}{\text{hyp}}$$?
Q5.Which of the following are equivalent to $$\tan(\theta°)=\frac{\text{opp}}{\text{adj}}$$?
Q6.Which of the following are equivalent to $$\sin(\theta°)=\frac{\text{opp}}{\text{hyp}}$$?
Assessment exit quiz
6 Questions
Q1.What trigonometric ratio would you use to work out the length $$k$$?

Q2.What trigonometric ratio would you use to work out the length $$b$$?

Q3.What trigonometric ratio would you use to work out the length $$e$$?

Q4.Work out the length $$b$$ to 1 decimal place.

Q5.Work out the length $$e$$ to 1 decimal place.

Q6.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 $$c$$.
50.2° - When $$a$$ = 6 cm and $$b$$ = 5 cm, angle $$x$$° is ...
30° - When $$a$$ = 6 cm and $$c$$ = 12 cm, angle $$x$$° is ...
60° - When $$b$$ = 4 cm and $$c$$ = 8 cm, angle $$x$$° is ...
63.4° - When $$a$$ = 2 cm and $$b$$ = 1 cm, angle $$x$$° is ...