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Chapter 6: Problem 26

Convert to radian measure. Round the answer to two decimal places. $$-231.2^{\circ}$$

Short Answer

Expert verified
-4.04

Step by step solution

01

Understand the Conversion Factor

To convert degrees to radians, use the conversion factor \( \frac{\pi}{180} \). This factor arises because \(180^\circ = \pi \text{ radians} \).
02

Apply the Conversion Factor

Multiply the angle in degrees by \( \frac{\pi}{180} \): \(-231.2^{\circ} \times \frac{\pi}{180} \).
03

Compute the Product

Perform the multiplication: \(-231.2 \times \frac{\pi}{180} \approx -4.035 \).
04

Round to Two Decimal Places

Round the result to two decimal places: \(-4.04 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Angle Measurement
Angles are a fundamental part of mathematics and physics. We measure angles to describe the rotation between two intersecting lines.

  • Angles are commonly measured in degrees or radians.
  • Degrees are more intuitive for everyday use, like in geometry or navigation.
  • Radians are often used in higher mathematics and physics because they simplify many formulas.

For example, a full circle is 360 degrees, but the same circle is also 2蟺 radians.
Conversion Factor
We need a method to convert between degrees and radians. This is where the conversion factor comes in.

  • The key conversion factor is \( \frac{ \pi }{180} \) when converting degrees to radians.
  • This is because there are \( 180^{ \circ } \) in \( \pi \) radians.

To convert degrees to radians, multiply the angle by this factor.
For instance, use \( -231.2^{ \circ } \times \frac{ \pi }{180} \).
Radian Measure
Radians are another way to measure angles, often used in mathematics. One radian represents the angle created when the arc length is equal to the radius.
  • The following formula helps in converting degrees to radians: \( \text{radians} = \text{degrees} \times \frac{\pi}{180} \)

Let鈥檚 apply this to \(-231.2^{ \circ }\):
Multiply: \( -231.2 \times \frac{ \pi }{180} \approx -4.035 \).
Round to two decimal places: \(- 4.04 \).

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Most popular questions from this chapter

Find the function value. Round to four decimal places. $$\sin \left(-16.4^{\circ}\right)$$

Find the reference angle and the exact function value if they exist. $$\sin \left(-450^{\circ}\right)$$

Find the function value. Round to four decimal places. $$\cos \left(-295.8^{\circ}\right)$$

Find the signs of the six trigonometric function values for the given angles. $$319^{\circ}$$

Given that \(\sin 82^{\circ}=p, \cos 82^{\circ}=q,\) and \(\tan 82^{\circ}=r,\) find the six function values of \(8^{\circ}\) in terms of \(p, q,\) and \(r\).
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