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

Checking and securing understanding of trigonometric ratios

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

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?

This lesson was made for home learning during the pandemic.

Drawing the sine and cosine graphs

Lesson outcome

This lesson was made for home learning during the pandemic.