Evaluate Sin 150 Degrees Without Using A Calculator

Method to Evaluate sin 150°

To find sin 150° without a calculator, we can use the following approach:

1. Identify the reference angle for 150°.
2. Determine the quadrant in which 150° lies.
3. Use the appropriate trigonometric identity based on the angle's position.
4. Calculate the sine value using known trigonometric values.

The reference angle for 150° is calculated as 180° - 150° = 30°. Since 150° is in the second quadrant, we know that sine is positive in this quadrant. We can use the identity sin(180° - θ) = sinθ to find sin 150°.

Step-by-Step Calculation

1. First, identify that 150° is in the second quadrant (90° to 180°).
2. Calculate the reference angle: 180° - 150° = 30°.
3. Recall that sin 30° = 0.5.
4. Since sine is positive in the second quadrant, sin 150° = sin 30° = 0.5.

Worked Example

Let's work through an example to find sin 150°:

1. Start with the angle: 150°.
2. Find the reference angle: 180° - 150° = 30°.
3. We know that sin 30° = 0.5.
4. Since 150° is in the second quadrant where sine is positive, sin 150° = 0.5.

The final result is sin 150° = 0.5.

Formula Used

This identity allows us to find the sine of an angle in the second quadrant by using the sine of its reference angle in the first quadrant.