What is the exact value of sin(π/6)?
Understand the Problem
The question is asking for the exact value of the sine function at the angle pi/6 radians. It requires knowing the sine values of commonly used angles in trigonometry.
Answer
$\frac{1}{2}$
Answer for screen readers
The exact value of $\sin\left(\frac{\pi}{6}\right)$ is $\frac{1}{2}$.
Steps to Solve
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Identify the angle in degrees To convert the angle from radians to degrees, use the conversion factor that $180^\circ$ is equivalent to $\pi$ radians. So, for the angle $\frac{\pi}{6}$: $$ \text{Degrees} = \frac{\pi}{6} \times \frac{180^\circ}{\pi} = 30^\circ $$
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Recall the sine value for the angle For the angle $30^\circ$, or equivalently $\frac{\pi}{6}$ radians, the sine value is a well-known trigonometric value: $$ \sin\left(\frac{\pi}{6}\right) = \frac{1}{2} $$
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Final output of the calculation We conclude that the sine of the angle $\frac{\pi}{6}$ in both radians and degrees is: $$ \sin\left(\frac{\pi}{6}\right) = \frac{1}{2} $$
The exact value of $\sin\left(\frac{\pi}{6}\right)$ is $\frac{1}{2}$.
More Information
The sine function is fundamental in trigonometry and has specific known values for certain key angles. The angle $\frac{\pi}{6}$ radians (or 30 degrees) corresponds to a right triangle where the ratio of the opposite side to the hypotenuse is always $\frac{1}{2}$.
Tips
- Confusing radians with degrees, leading to incorrect sine values.
- Forgetting the special angles in trigonometry, which can lead to oversight of knowing $\sin\left(\frac{\pi}{6}\right)$ is $\frac{1}{2}$.
