What is the exact value of sin 150?
Understand the Problem
The question is asking for the exact value of the sine function evaluated at 150 degrees. This involves using the properties of the sine function to find the sine value for this specific angle.
Answer
$\frac{1}{2}$
Answer for screen readers
The exact value of $\sin(150^\circ)$ is $\frac{1}{2}$.
Steps to Solve
- Identify the Reference Angle
To find $\sin(150^\circ)$, first identify the reference angle. The reference angle for $150^\circ$ is $180^\circ - 150^\circ = 30^\circ$.
- Determine the Quadrant
Since $150^\circ$ is in the second quadrant, where the sine function is positive, we use the sine value of the reference angle.
- Use the Sine Value of the Reference Angle
Now we find $\sin(30^\circ)$. The value is known from trigonometric ratios: $$ \sin(30^\circ) = \frac{1}{2} $$
- Final Calculation for Sine
Since $\sin(150^\circ)$ refers to the sine of the reference angle 30 degrees and remains positive in the second quadrant: $$ \sin(150^\circ) = \sin(30^\circ) = \frac{1}{2} $$
The exact value of $\sin(150^\circ)$ is $\frac{1}{2}$.
More Information
The sine function is a periodic function, and the values at specific angles (like 30°, 45°, and 60°) are commonly used in trigonometry. Knowing these values can help simplify calculations.
Tips
- Confusing reference angles: Make sure to correctly subtract from $180^\circ$ for angles in the second quadrant.
- Forgetting the sign of sine in different quadrants: Remember that sine is positive in the first and second quadrants.
