What is the value of sin 150 degrees?

Sin 150 degrees refers to the sine of the angle 150 degrees. To find its value, we need to use the concept of trigonometry. Trigonometry is a branch of mathematics that deals with the relationship between angles and the sides of a triangle.

In a unit circle, which is a circle with a radius of 1, we can measure angles starting from the positive x-axis and moving counterclockwise. The sine function, denoted as sin, represents the ratio of the length of the side opposite to the angle to the hypotenuse of a right triangle. In trigonometry, angles are often measured in degrees.

Now, let’s calculate the value of sin 150 degrees.

To visualize this angle, we can draw a unit circle and place the angle of 150 degrees in the Cartesian coordinate system. The angle intersects the unit circle at a point, let’s call it P.

By drawing a vertical line segment from point P to the x-axis, we create a right triangle. The side adjacent to the angle is the horizontal distance from point P to the y-axis, which we can determine as √3/2, and the hypotenuse, which is always 1 in a unit circle.

Now, we can apply the sine function to find the value of sin 150 degrees:

sin 150 degrees = Opposite/Hypotenuse = √3/2.

FAQs about the sine of 150 degrees:

1. What is the sine of 150 degrees in fraction form?

The sine of 150 degrees is √3/2.

2. Can the sine of 150 degrees be simplified further?

No, √3/2 is already in its simplest form.

3. What is the decimal approximation of sin 150 degrees?

The decimal approximation of √3/2 is approximately 0.866.

4. Is the sine of 150 degrees positive or negative?

The sine of 150 degrees is positive because the angle falls in the second quadrant, where the sine function is positive.

5. How is sin 150 degrees related to sin 30 degrees?

Sin 150 degrees is the value obtained by reflecting sin 30 degrees across the y-axis. Therefore, sin 150 degrees is equal to sin 30 degrees, which is 1/2.

6. What is the value of cos 150 degrees?

The value of cos 150 degrees can be found using the complementary angle property of trigonometry. Cos 150 degrees is equal to -cos 30 degrees, which is -√3/2.

7. Can the sine of 150 degrees be negative?

No, the sine of 150 degrees is always positive because it lies in the second quadrant of the unit circle.

8. How does sin 150 degrees relate to sin 210 degrees?

Sin 150 degrees is the negative value of sin 210 degrees since they are symmetrical across the y-axis.

9. What is the relationship between sin 150 degrees and sin 330 degrees?

Sin 150 degrees and sin 330 degrees are negative reciprocals of each other.

10. What is the sine of the supplementary angle to 150 degrees?

The supplementary angle to 150 degrees is 180 degrees. Since sin 150 degrees equals sin 30 degrees, sin 180 degrees is also 0, making them equal.

11. How does the sine of 150 degrees compare to the sine of 120 degrees?

The sine of 150 degrees is √3/2, while the sine of 120 degrees is √3/2. Therefore, both angles have the same sine value.

12. Are there any applications where sin 150 degrees is useful?

The calculation of sin 150 degrees and other trigonometric functions is extensively used in various fields such as engineering, physics, computer graphics, and navigation systems to determine angles, distances, and trajectories.

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