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Quick Quiz: Understanding the Sine, Cosine, Tangent Definitions

Hey there, future math whizzes! 👋 Ready to test your knowledge of sine, cosine, and tangent? These trig functions are super important for understanding angles and triangles. Let's dive into a quick study guide and then challenge ourselves with a practice quiz! 🤓
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baker.meredith62 Jan 3, 2026

📚 Quick Study Guide

    📐
  • Sine (sin): The ratio of the length of the opposite side to the length of the hypotenuse in a right triangle. $\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}$
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  • Cosine (cos): The ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle. $\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}}$
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  • Tangent (tan): The ratio of the length of the opposite side to the length of the adjacent side in a right triangle. $\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}}$
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  • SOH CAH TOA: A mnemonic to remember the definitions: Sine is Opposite over Hypotenuse, Cosine is Adjacent over Hypotenuse, Tangent is Opposite over Adjacent.
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  • Angle of Elevation: The angle formed by a horizontal line and the line of sight to an object above the horizontal line.
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  • Angle of Depression: The angle formed by a horizontal line and the line of sight to an object below the horizontal line.
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  • Reciprocal Identities: Cosecant (csc), Secant (sec), and Cotangent (cot) are reciprocals of Sine, Cosine, and Tangent respectively. $\csc(\theta) = \frac{1}{\sin(\theta)}$, $\sec(\theta) = \frac{1}{\cos(\theta)}$, $\cot(\theta) = \frac{1}{\tan(\theta)}$

🤔 Practice Quiz

  1. What is the sine of an angle in a right triangle defined as?
    1. Adjacent / Hypotenuse
    2. Opposite / Adjacent
    3. Opposite / Hypotenuse
    4. Hypotenuse / Opposite
  2. What is the cosine of an angle in a right triangle defined as?
    1. Opposite / Hypotenuse
    2. Adjacent / Hypotenuse
    3. Opposite / Adjacent
    4. Hypotenuse / Opposite
  3. What is the tangent of an angle in a right triangle defined as?
    1. Adjacent / Hypotenuse
    2. Opposite / Hypotenuse
    3. Opposite / Adjacent
    4. Hypotenuse / Opposite
  4. In a right triangle, if the opposite side is 3 and the hypotenuse is 5, what is the sine of the angle?
    1. 3/4
    2. 4/5
    3. 3/5
    4. 5/3
  5. In a right triangle, if the adjacent side is 4 and the hypotenuse is 5, what is the cosine of the angle?
    1. 3/5
    2. 4/5
    3. 3/4
    4. 5/4
  6. In a right triangle, if the opposite side is 3 and the adjacent side is 4, what is the tangent of the angle?
    1. 4/5
    2. 3/5
    3. 4/3
    4. 3/4
  7. Which mnemonic helps in remembering the definitions of sine, cosine, and tangent?
    1. TOA CAH SOH
    2. SOH CAH TOA
    3. CAH SOH TOA
    4. SOH TOA CAH
Click to see Answers
  1. C
  2. B
  3. C
  4. C
  5. B
  6. D
  7. B

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