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.

Calculate trigonometric ratios for 30° and 60°

Maths

In this unit, pupils have explored the trigonometric ratios for right-angled triangles in a variety of situations. In the future unit, pupils explore what can be done when we have a triangle that is not right-angled.

In the prior unit, pupils were introduced to the trigonometric ratios and developed the skills to ascertain which ratio would be appropriate for a given problem. In this unit, pupils are introduced to a variety of situations where this knowledge is required, such as 3-D problems and elevation/depression.

Right-angled trigonometry

Which type of triangle can help deduce the exact trigonometric ratios for $$30^\circ$$ and $$60^\circ$$?

What is the exact value of $$\cos(30^\circ)$$?

What is the exact value of $$\sin(60^\circ)$$?

What is the exact value of $$\tan(60^\circ)$$?

What is the exact value of $$\cos(60^\circ)+\sin(30^\circ)$$?

What is the exact value of $$\sin(60^\circ)\times\tan(30^\circ)$$?

Three trigonometric ratios are sine, cosine and {{}}.

Lucas has used his calculator to work out the value of $$\cos(48^\circ)$$. What is the value to 2 decimal places?

Izzy has used her calculator to answer a trigonometry question. What is the length of the hypotenuse?

Laura has used her calculator to answer a trigonometry question. What is the length of the adjacent?

Used sine when he should have used tangent.

Used sine when he should have used cosine. 

Forgotten to have his angle in the calculation.

Inputted the lengths for the opposite and hypotenuse the wrong way around.

Andeep has attempted to use his calculator to answer a trigonometry question but has found himself with this message on his calculator. What might he have done wrong?

Which calculations are correct to find the length marked $$x$$?

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