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.

Drawing the sine and cosine graphs

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

The __________ allows us to work out values for $$\sin(\theta°)$$ and $$\cos(\theta°)$$. 

Go to settings and change from radians to degrees.

Go to settings and change the $$x$$ axis interval to $$ 0°\leq x\leq 360°$$.

Go to settings and change the $$y$$ axis interval to $$ 0°\leq y\leq 360°$$.

Andeep wants a sine graph from 0° to 360°. He opened Desmos and typed in "y=sin(x)". This image appears. What does Andeep need to do to see the sine graph between 0° and 360° degrees?

Go to settings and change the $$x$$ axis interval to $$ -1\leq x\leq 1$$.

Go to settings and change the $$y$$ axis interval to $$ -1\leq y\leq 1$$.

Andeep wants a sine graph from 0° to 360°. He opened Desmos and typed in "y=sin(x)". This image appears. What does Andeep need to do to see the full sine graph between 0° and 360°?

Using Desmos and an $$x$$ axis interval of $$ 0°\leq x\leq 360°$$, how many times does the sine graph pass through the $$x$$ axis?

Using Desmos and an $$x$$ axis interval of $$ 0°\leq x\leq 360°$$, how many times does the cosine graph pass through the $$x$$ axis?

Using Desmos and an $$x$$ axis interval of $$ 0°\leq x\leq 360°$$, what are the $$x$$ coordinates of the intersections of $$y = \sin(x°)$$ and $$y = \cos(x°)$$?

$$y$$-coordinate (P) on the triangle formed inside the unit circle.

$$x$$-coordinate (P) on the triangle formed inside the unit circle.

line that intersects the circle exactly once.

Match the trigonometric ratio with the correct definition.

A right-angled triangle is drawn and an angle $$x$$ is indicated. The opposite length is 3 cm and the adjacent length is 2 cm. Work out the angle $$x$$°. Give your answer to 1 decimal place.

A right-angled triangle is drawn and an angle $$x$$ is indicated. The opposite length is 8 cm and the hypotenuse length is 16 cm. Work out the angle $$x$$°.

Jun draws a square with lengths 7 cm. What is the angle between the diagonals and the length 7 cm?

Starter Quiz