Final answer:
The value of cos 150° is -√3/2, which can be found using the trigonometric identity sin² θ + cos² θ = 1 and recognizing that cosine is negative in the second quadrant.
Step-by-step explanation:
The value of cos 150° can be determined without the use of a calculator by understanding the properties of trigonometric functions in different quadrants. Since 150° is in the second quadrant where sine is positive and cosine is negative, and using the fact that sin 150° = 0.5, we can find cos 150° using the Pythagorean identity sin² θ + cos² θ = 1.
First, we calculate sin² 150°:
- sin² 150° = (0.5)² = 0.25
Then, we use the Pythagorean identity to find cos² 150°:
- 1 - sin² 150° = cos² 150°
- 1 - 0.25 = cos² 150°
- 0.75 = cos² 150°
Since cosine is negative in the second quadrant, cos 150° is the negative square root of 0.75. Therefore:
- cos 150° = -√0.75
Exact values can be determined by recognizing that √0.75 is the same as √(3/4), which simplifies to √3/2. Thus:
- cos 150° = -√3/2
In summary, the value of cos 150° is -√3/2.