Multiple Choice
How many radians is ?
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1. Measuring Angles
Radians
Multiple Choice
Which of the following lists all the exact solutions in radians to the equation ?
A
, where is any integer
B
, where is any integer
C
, where is any real number
D
, where is any integer
Verified step by step guidance1
Recall the general solutions for the equation \( \sin x = 0 \). The sine function equals zero at integer multiples of \( \pi \), that is, \( x = k\pi \) where \( k \) is any integer.
Understand that the sine function has zeros at \( 0, \pi, 2\pi, 3\pi, \ldots \) and also at their negative counterparts \( -\pi, -2\pi, -3\pi, \ldots \). This pattern repeats every \( \pi \) radians.
Express the solution set as \( x = k\pi \), where \( k \in \mathbb{Z} \) (the set of all integers), to include all these points.
Note that solutions like \( x = 0 + k\pi \) and \( x = k\pi \) are equivalent ways to write the same solution set, emphasizing the periodicity of sine zeros.
Avoid solutions involving fractions like \( \frac{\pi}{2} + k\pi \) because sine equals \( \pm 1 \) at those points, not zero.
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