Textbook Question
Convert each radian measure to degrees. Write answers to the nearest minute. See Example 2(c).
9.84763
1
views
Ch. 3 - Radian Measure and The Unit Circle
Lial12th EditionTrigonometryISBN: 9780136552161
Not the one you use?Change textbookSelect a different textbook
Table of contents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Chapter 4, Problem 63
Convert each radian measure to degrees. Write answers to the nearest minute. See Example 2(c).
-5.01095
Verified step by step guidance1
Recall the conversion formula between radians and degrees: \(\text{degrees} = \text{radians} \times \dfrac{180}{\pi}\).
Multiply the given radian measure, \(-5.01095\), by \(\dfrac{180}{\pi}\) to convert it to degrees: \(-5.01095 \times \dfrac{180}{\pi}\).
Calculate the decimal degree value from the multiplication (do not round yet).
Separate the decimal degree value into its whole number part (degrees) and the fractional part.
Convert the fractional part of the degrees into minutes by multiplying it by 60, then round to the nearest whole minute.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Was this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Radian to Degree Conversion
Radians and degrees are two units for measuring angles. To convert radians to degrees, multiply the radian measure by 180/π. This conversion is essential because degrees are often easier to interpret and are commonly used in practical applications.
Recommended video:
5:04
Converting between Degrees & Radians
Degree, Minutes, and Seconds
Degrees can be subdivided into minutes and seconds, where 1 degree equals 60 minutes and 1 minute equals 60 seconds. Writing answers to the nearest minute means converting the decimal part of degrees into minutes by multiplying by 60 and rounding appropriately.
Recommended video:
5:04Converting between Degrees & Radians
Rounding and Precision
When converting and expressing angles, rounding to the nearest minute requires careful handling of decimal values to maintain accuracy. This ensures the final answer is precise and consistent with the required format, avoiding errors in interpretation.
Recommended video:
2:22Cardioids Example 1
Related Practice
Textbook Question
Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement true.
sin s = 0.9918
Textbook Question
Find the approximate value of s, to four decimal places, in the interval [0 , π/2] that makes each statement true.
sec s = 1.0806
1
views
Textbook Question
Find each exact function value. See Example 3.
sin π/3
1
views
Textbook Question
Find the exact value of s in the given interval that has the given circular function value.
[π/2, π] ; sin s = 1/2
Textbook Question
Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement true.
cos s = 0.7826