Recognize Problem: Recognize that the equation Sin x = 1/2 is asking for the angle(s) x for which the sine function has a value of 1/2. We know from trigonometry that the sine function has a value of 1/2 at specific standard angles.Recall Unit Circle: Recall the unit circle and the values of sine for standard angles. The sine of an angle is 1/2 at angles of 30 degrees (π/6 radians) and 150 degrees (5π/6 radians) in the first and second quadrants, respectively, where the sine function is positive.Convert Angles: Convert the known angles to radians if necessary. Since the sine function is periodic, we also need to consider all angles coterminal with 30 degrees and 150 degrees. The general solution for x where Sin x = 1/2 is x = π/6 + 2nπ and x = 5π/6 + 2nπ, where n is any integer.

Resources

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

If $\sin x = \frac{1}{2}$ , $x = ?$

View step-by-step help

Home

Math Problems

Grade 8

Solve equations: mixed review

Full solution

Q. If

\sin x = \frac{1}{2}

x = ?

Recognize Problem: Recognize that the equation $\sin x = \frac{1}{2}$ is asking for the angle(s) $x$ for which the sine function has a value of $\frac{1}{2}$ . We know from trigonometry that the sine function has a value of $\frac{1}{2}$ at specific standard angles.
Recall Unit Circle: Recall the unit circle and the values of sine for standard angles. $\newline$ The sine of an angle is $\frac{1}{2}$ at angles of $30$ degrees ( $\frac{\pi}{6}$ radians) and $150$ degrees ( $\frac{5\pi}{6}$ radians) in the first and second quadrants, respectively, where the sine function is positive.
Convert Angles: Convert the known angles to radians if necessary. $\newline$ Since the sine function is periodic, we also need to consider all angles coterminal with $30$ degrees and $150$ degrees. $\newline$ The general solution for $x$ where $\sin x = \frac{1}{2}$ is $x = \frac{\pi}{6} + 2n\pi$ and $x = \frac{5\pi}{6} + 2n\pi$ , where $n$ is any integer.