Podcast
Questions and Answers
What is the name of the longest side of a right-angled triangle?
What is the name of the longest side of a right-angled triangle?
- Opposite side
- Base
- Hypotenuse (correct)
- Adjacent side
Which trigonometric ratio corresponds to the formula sin x = opposite / hypotenuse?
Which trigonometric ratio corresponds to the formula sin x = opposite / hypotenuse?
- Cosecant
- Tangent
- Sine (correct)
- Cosine
What is the value of sin 30°?
What is the value of sin 30°?
- 1
- 1/2 (correct)
- √3/2
- √3
In relation to angle x, which side is referred to as the adjacent side?
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°?
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?
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 expression represents the tangent ratio based on the sides of a right triangle?
What is the cosine value for angle 60°?
What is the cosine value for angle 60°?
Flashcards
Hypotenuse
Hypotenuse
The longest side of a right-angled triangle, opposite the right angle.
Opposite Side
Opposite Side
The side opposite the angle in question, labeled o in a right-angled triangle.
Adjacent Side
Adjacent Side
The side next to the angle in question, labeled a in a right-angled triangle.
Sine
Sine
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Cosine
Cosine
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Tangent
Tangent
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Equilateral Triangle split into two right-angled triangles
Equilateral Triangle split into two right-angled triangles
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Square split into two right-angled triangles
Square split into two right-angled triangles
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Study Notes
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.
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Description
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.
