Calculate trigonometric ratios for 0°, 45° and 90° | Maths

Starter quiz

A right-angled isosceles triangle has...

... two $45^\circ$ angles and a right-angle. ✓

... three different edge lengths.

... a hypotenuse $\sqrt{2}$ times longer than the other two edges. ✓

... two right-angles and one other angle.
$What is the exact value of <Math>\cos(45^\circ)</Math>?$

What is the exact value of $\cos(45^\circ)$ ?

$\frac{1}{\sqrt{2}}$ ✓

$1$

$\sqrt{2}$

$\frac{\sqrt{2}}{2}$ ✓
$What is the exact value of <Math>\tan(45^\circ)</Math>?$

What is the exact value of $\tan(45^\circ)$ ?

$\frac{1}{\sqrt{2}}$

$1$ ✓

$\sqrt{2}$

$\frac{\sqrt{2}}{2}$
What does this diagram show?

$\sin(0^\circ)=1$

$\sin(0^\circ)=0$ ✓

$\cos(0^\circ)=0$

$\cos(0^\circ)=1$ ✓

$\tan(0^\circ)=0$ ✓
$This diagram shows that <Math>\sin(90^\circ)=1</Math> and <Math>\cos(90^\circ)=0</Math>, but what is <Math>\tan(90^\circ)</Math>?$

This diagram shows that $\sin(90^\circ)=1$ and $\cos(90^\circ)=0$ , but what is $\tan(90^\circ)$ ?

0 as there is not an answer.

undefined as the line does not intersect the tangent. ✓

1 as the tangent is $x=1$
What is the exact value of $\tan(45^\circ)+\sin(90^\circ)$ ?

'2' ✓

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The trigonometric ratios for 45° can be calculated using a square
The square should have lengths of 1 unit
By splitting the square into two right-angled triangles, you can calculate the ratio
The ratios for 0° and 90° can be reasoned

Trigonometry always involves rounding.

Try evaluating sin(0) 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.