Quick Quiz: Understanding the Sine, Cosine, Tangent Definitions

📚 Quick Study Guide

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• 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