Trigonometry: Trigonometric Ratios Quiz

What is the name of the longest side of a right-angled triangle?

Which trigonometric ratio corresponds to the formula sin x = opposite / hypotenuse?

What is the value of sin 30°?

In relation to angle x, which side is referred to as the adjacent side?

Using a square of side lengths 1 cm, what is the trigonometric ratio for sin 45°?

If a right-angled triangle has an opposite side of length 3 cm and a hypotenuse of length 5 cm, what is sin x?

What expression represents the tangent ratio based on the sides of a right triangle?

What is the cosine value for angle 60°?

Trigonometric Ratios

Trigonometry is used to calculate angles and sides in triangles.
Right-angled triangles have three sides:
- Hypotenuse (h): The longest side, opposite the right angle.
- Opposite (o): Opposite the angle in question.
- Adjacent (a): Next to the angle in question.

Three Trigonometric Ratios

Sine (sin), Cosine (cos), and Tangent (tan) are three trigonometric ratios.
These ratios are calculated by comparing the sides of a right-angled triangle to a specific angle.
Formulas:
- sin x = opposite / hypotenuse
- cos x = adjacent / hypotenuse
- tan x = opposite / adjacent

Exact Trigonometric Ratios for Specific Angles

Special triangles (e.g., equilateral triangles) can be used to determine exact values for trigonometric ratios of specific angles (30°, 45°, 60°, 90°).
Pythagoras' Theorem can be used to calculate the length of the third side of a right-angled triangle if two sides are known.
Example ratios:
- sin 30° = 1/2
- cos 30° = √3/2
- tan 30° = 1/√3
- sin 60° = √3/2
- cos 60° = 1/2
- tan 60° = √3
- sin 45° = 1/√2
- cos 45° = 1/√2
- tan 45° = 1

Calculating Missing Sides

A square can be split into two right-angled triangles to calculate trigonometric ratios of 45° angles.
Pythagoras' theorem (a² + b² = c²) allows calculating the length of the third side of a right-angled triangle, given the other two sides.

Test your knowledge of trigonometric ratios related to right-angled triangles. This quiz covers sine, cosine, and tangent calculations, as well as exact values for specific angles. Perfect for students learning trigonometry concepts in mathematics.