Value of Sin 30 Degree

Sin 30°

The value of sin 30 degrees is 0.5. When expressed in radians, sin 30 degrees is written as sin(30° / 180°), which simplifies to sin(π/6) or sin(0.523598...). In this article, we will explain how to determine the value of sin 30 degrees with examples.

• Sin 30°: 0.5
• Sin 30° as a fraction: 1/2
• Sin (-30°): -0.5
• Sin 30° in radians: sin(π/6) or sin(0.523598...)

Also Check: Value of Sin 60 Degree

What is Sin 30 Degrees?

The sine of 30 degrees is equal to 0.5. To express this angle in radians, we use the conversion factor where radians = degrees × (π/180). Therefore, 30 degrees is equal to 30 × (π/180) radians, which simplifies to π/6 or approximately 0.5236 radians. Hence, sin 30° = sin(0.5236) = 1/2 or 0.5.

• The sine of 30 degrees is 0.5.
• To convert 30 degrees to radians, use the formula radians = degrees × (π/180).
• Thus, 30 degrees = 30 × (π/180) radians, which simplifies to π/6 or approximately 0.5236 radians.
• Therefore, sin 30° = sin(0.5236) = 0.5.

Explanation:

In the first quadrant, where angles range from 0° to 90°, the sine of 30° is positive. Specifically, sin 30° equals 1/2 or 0.5 due to the sine function's positivity in this quadrant. The sine of 30° also repeats periodically with an angle of 360° added to multiples, denoted as sin 30° = sin(30° + 360°n), where n is any integer. Thus, sin 30° = sin 390° = sin 750°, and so forth.

Additionally, for negative angles like -30°, the sine function behaves according to its odd nature: sin(-30°) = -sin(30°).

Also Check: Value of Sin 45 Degree

Methods to Find Value of Sin 30 Degrees

In the first quadrant, the sine function is positive. Sin 30° is assigned a value of 0.5. The value of sin 30
degrees can be found by:

• Utilizing the Unit Circle
• Trigonometric Functions in Action

Understanding the Unit Circle:

The unit circle is crucial in trigonometry as it provides a way to understand trigonometric functions geometrically. For any point (x, y) on the unit circle, the coordinates (x, y) represent cos θ and sin θ respectively, where θ is the angle formed between the positive x-axis and the radius (line segment from the origin to the point).

Finding sin 30° Using the Unit Circle:

To find sin 30°, start by understanding where 30° falls on the unit circle.

30° is located in the first quadrant, where both x and y coordinates are positive.

Rotate counterclockwise from the positive x-axis to form a 30° angle.

This rotation intersects the unit circle at a point (x, y) where x = cos 30° and y = sin 30°.

Determining the Coordinates:

At 30°, the coordinates of the unit circle are (cos 30°, sin 30°).

The cosine of 30°, cos 30°, is known to be approximately 0.866.

The sine of 30°, sin 30°, corresponds to the y-coordinate at this point.

Calculating sin 30°:

According to trigonometric values, sin 30° = 0.5.

This value corresponds to the y-coordinate of the point on the unit circle where the angle of 30° intersects.

Sine of 30 Degrees in Terms of Trigonometric Functions

• \( \sin 30^\circ = \pm \sqrt{1 - \cos^2 30^\circ} \)
• \( \sin 30^\circ = \pm \frac{\tan 30^\circ}{\sqrt{1 + \tan^2 30^\circ}} \)
• \( \sin 30^\circ = \pm \frac{1}{\sqrt{1 + \cot^2 30^\circ}} \)
• \( \sin 30^\circ = \pm \sqrt{\sec^2 30^\circ - 1} \cdot \sec 30^\circ \)
• \( \sin 30^\circ = \frac{1}{\csc 30^\circ} \)

Note: Since \( 30^\circ \) is in the first quadrant, its final value will be positive.

To find the value of sin 30° using trigonometric identities, we can use the following equivalences: sin(180° - 30°) = sin 150° -sin(180° + 30°) = -sin 210° cos(90° - 30°) = cos 60° -cos(90° + 30°) = -cos 120°