Trigonometry quiz
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What function is sine divided by cosine?
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More questions about Trigonometry
These visible examples show the question style. LearnClash turns the full topic into ranked duels and spaced repetition.
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How big can the sine of an angle get?
Answer: 1
Why: The hypotenuse is a right triangle's longest side, so opposite over hypotenuse stays below 1 for every acute angle.
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At which angle is the tangent undefined?
Answer: 90°
Why: Just below 90° tangent explodes: $\tan 89°$ is already about 57, and it grows without limit as the angle closes in.
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Which part of a circle did early Indian sine values halve?
Answer: A chord
Why: In a circle of radius 1, half the chord across a central angle of 2θ is exactly $\sin\theta$ long.
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What is the angle from the horizontal up to a treetop called?
Answer: Angle of elevation
Why: Looking back down from the treetop gives the angle of depression, and the two angles are always equal.
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Which shape lets sine and cosine work past 90°?
Answer: Unit circle
Why: At angle θ the point sits at $(\cos\theta, \sin\theta)$, so past 90° its x-coordinate, the cosine, turns negative.
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Whose formula simplifies $(\cos x + i\sin x)^n$?
Answer: De Moivre
Why: De Moivre's formula makes finding complex roots straightforward by dividing the angle evenly around a circle.
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