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QUESTION 6Convert the angle in degrees to radians. Express the answer as multiple of .-90 - - - -

Question

QUESTION 6

Convert the angle in degrees to radians. Express the answer as multiple of .

-90 - - - -

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Solution

1. Break Down the Problem

To convert an angle from degrees to radians, we need to identify the degree measure and apply the conversion formula. The formula for this conversion is given by: radians=degrees×(π180) \text{radians} = \text{degrees} \times \left(\frac{\pi}{180}\right) In this case, the angle is 90-90 degrees.

2. Relevant Concepts

Using the formula mentioned:

  1. We need to substitute 90-90 for degrees.
  2. We need to simplify the result to express it in terms of π\pi.

3. Analysis and Detail

Substituting the value into the formula: radians=90×(π180) \text{radians} = -90 \times \left(\frac{\pi}{180}\right) Next, we simplify the expression: radians=90π180 \text{radians} = -\frac{90\pi}{180} This further simplifies to: radians=π2 \text{radians} = -\frac{\pi}{2}

4. Verify and Summarize

The angle of 90-90 degrees converts to radians as π2-\frac{\pi}{2}. This verifies our calculations.

Final Answer

The angle 90-90 degrees in radians is: π2 -\frac{\pi}{2}

This problem has been solved

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