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Which of the following has value zero:...

Which of the following has value zero:

A

`sin0^circ`

B

`tan0^circ`

C

`cos0^circ`

D

`cot0^circ`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question "Which of the following has value zero?", we will evaluate the trigonometric functions at the angle of 0 degrees (or 0 radians). ### Step-by-Step Solution: 1. **Evaluate sin(0)**: - The sine function at 0 degrees is defined as: \[ \sin(0) = 0 \] 2. **Evaluate cos(0)**: - The cosine function at 0 degrees is defined as: \[ \cos(0) = 1 \] 3. **Evaluate tan(0)**: - The tangent function is defined as the ratio of sine to cosine: \[ \tan(0) = \frac{\sin(0)}{\cos(0)} = \frac{0}{1} = 0 \] 4. **Evaluate cot(0)**: - The cotangent function is defined as the ratio of cosine to sine: \[ \cot(0) = \frac{\cos(0)}{\sin(0)} = \frac{1}{0} \] - Since division by zero is undefined, cot(0) does not have a value. 5. **Conclusion**: - From the evaluations, we find that: - \(\sin(0) = 0\) - \(\tan(0) = 0\) - \(\cot(0)\) is undefined - \(\cos(0) = 1\) - Therefore, the functions that have a value of zero are \(\sin(0)\) and \(\tan(0)\). ### Final Answer: The functions that have a value of zero are **sin(0)** and **tan(0)**.

To solve the question "Which of the following has value zero?", we will evaluate the trigonometric functions at the angle of 0 degrees (or 0 radians). ### Step-by-Step Solution: 1. **Evaluate sin(0)**: - The sine function at 0 degrees is defined as: \[ \sin(0) = 0 ...
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