Trigonometric ratios
9 flashcards to master Trigonometric ratios
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In a right-angled triangle, angle θ is given. If the opposite side is 6 and the hypotenuse is 10, what is sin(θ)?
sin(θ) = Opposite/Hypotenuse. Therefore, sin(θ) = 6/10 = 0.6
Define the term 'adjacent' in the context of trigonometric ratios.
The adjacent side is the side next to the given angle (θ) in a right-angled triangle, that is not the hypotenuse. It forms one of the rays of the angle.
Explain the difference between 'angle of elevation' and 'angle of depression'.
Angle of elevation is the angle from the horizontal upwards to a point of interest. Angle of depression is the angle from the horizontal downwards to a point of interest.
A ladder leans against a wall. The angle of elevation from the ground to the top of the ladder is 60 degrees. What trig ratio relates the ladder's length and the wall's height?
Sine (sin) relates the opposite (wall height) to the hypotenuse (ladder's length). sin(60) = wall height/ladder length.
If cos(x) = 0.8 and the adjacent side is 8, what is the length of the hypotenuse?
Since cos(x) = Adjacent/Hypotenuse, 0.8 = 8/Hypotenuse. Therefore, Hypotenuse = 8/0.8 = 10.
When would you use the tangent ratio (tan)?
You would use the tangent ratio (tan) when you know, or need to find, the lengths of the opposite and adjacent sides of a right-angled triangle relative to a given angle.
A building casts a shadow of 20m when the angle of elevation of the sun is 30 degrees. How tall is the building?
We can use tan(30) = height/20. Therefore height = 20 * tan(30) ≈ 11.55m.
Key Questions: Trigonometric ratios
Define the term 'adjacent' in the context of trigonometric ratios.
The adjacent side is the side next to the given angle (θ) in a right-angled triangle, that is not the hypotenuse. It forms one of the rays of the angle.
Explain the difference between 'angle of elevation' and 'angle of depression'.
Angle of elevation is the angle from the horizontal upwards to a point of interest. Angle of depression is the angle from the horizontal downwards to a point of interest.
About Trigonometric ratios (6.1)
These 9 flashcards cover everything you need to know about Trigonometric ratios for your Cambridge IGCSE Mathematics (0580) exam. Each card is designed based on the official syllabus requirements.
What You'll Learn
- 4 Definitions - Key terms and their precise meanings that examiners expect
- 1 Key Concepts - Core ideas and principles from the 0580 syllabus
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After mastering Trigonometric ratios, explore these related topics:
- 5.4 Volume - 9 flashcards
- 6.2 Sine and cosine rules - 9 flashcards
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