Calculate trigonometric ratios for 30° and 60° | Maths

Starter quiz

Three trigonometric ratios are sine, cosine and ______.

'tangent' ✓
$Lucas has used his calculator to work out the value of <Math>\cos(48^\circ)</Math>. What is the value to 2 decimal places?$

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

'0.67' ✓
Izzy has used her calculator to answer a trigonometry question. What is the length of the hypotenuse?

$\sin(54)$

2.427050983

3 ✓
Laura has used her calculator to answer a trigonometry question. What is the length of the adjacent?

5 ✓

7.197782698

$\cos(46)$
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?

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

$x=\sqrt{9^2-8^2}$ ✓

$x=\frac{9}{\sin(63^\circ)}$

$x=\frac{9}{\cos(63^\circ)}$

$x=9\cos(63^\circ)$ ✓

$x=\frac{8}{\tan(63^\circ)}$ ✓

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

scalene triangle

isosceles triangle

equilateral triangle ✓
$What is the exact value of <Math>\cos(30^\circ)</Math>?$

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

$\frac{1}{2}$

$\frac{\sqrt{3}}{2}$ ✓

$\frac{1}{\sqrt{3}}$

$\frac{2}{\sqrt{3}}$

$\sqrt{3}$
$What is the exact value of <Math>\sin(60^\circ)</Math>?$

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

$\frac{1}{2}$

$\frac{\sqrt{3}}{2}$ ✓

$\frac{1}{\sqrt{3}}$

$\frac{2}{\sqrt{3}}$

$\sqrt{3}$
$What is the exact value of <Math>\tan(60^\circ)</Math>?$

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

$\frac{1}{2}$

$\frac{\sqrt{3}}{2}$

$\frac{1}{\sqrt{3}}$

$\frac{2}{\sqrt{3}}$

$\sqrt{3}$ ✓
What is the exact value of $\cos(60^\circ)+\sin(30^\circ)$ ?

'1' ✓
What is the exact value of $\sin(60^\circ)\times\tan(30^\circ)$ ?

'0.5' ✓

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The trigonometric ratios for 30° and 60° can be calculated using an equilateral triangle
The triangle should have lengths of 2 units
By splitting the triangle into two right-angled triangles, you can calculate the ratios

Trigonometry always involves rounding.

Try evaluating sin(30) on your calculator. What answer do you get?

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.