Sin 270 Degrees

The value of sin 270 degrees is -1. Sin 270 degrees in radians is written as sin (270° × π/180°), i.e., sin (3π/2) or sin (4.712388. . .). In this article, we will discuss the methods to find the value of sin 270 degrees with examples.

• Sin 270°: -1
• Sin (-270 degrees): 1
• Sin 270° in radians: sin (3π/2) or sin (4.7123889 . . .)

What is the Value of Sin 270 Degrees?

The value of sin 270 degrees is -1. Sin 270 degrees can also be expressed using the equivalent of the given angle (270 degrees) in radians (4.71238 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 270 degrees = 270° × (π/180°) rad = 3π/2 or 4.7123 . . .
∴ sin 270° = sin(4.7123) = -1

Explanation:

For sin 270 degrees, the angle 270° lies on the negative y-axis. Thus, sin 270° value = -1
Since the sine function is a periodic function, we can represent sin 270° as, sin 270 degrees = sin(270° + n × 360°), n ∈ Z.
⇒ sin 270° = sin 630° = sin 990°, and so on.
Note: Since, sine is an odd function, the value of sin(-270°) = -sin(270°).

Methods to Find Value of Sin 270 Degrees

The value of sin 270° is given as -1. We can find the value of sin 270 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 270 Degrees Using Unit Circle

To find the value of sin 270 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 270° angle with the positive x-axis.
• The sin of 270 degrees equals the y-coordinate(-1) of the point of intersection (0, -1) of unit circle and r.

Hence the value of sin 270° = y = -1

Sin 270° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 270 degrees as:

• ± √(1-cos²(270°))
• ± tan 270°/√(1 + tan²(270°))
• ± 1/√(1 + cot²(270°))
• ± √(sec²(270°) - 1)/sec 270°
• 1/cosec 270°

Note: Since 270° lies on the negative y-axis, the final value of sin 270° will be negative.

We can use trigonometric identities to represent sin 270° as,

• sin(180° - 270°) = sin(-90°)
• -sin(180° + 270°) = -sin 450°
• cos(90° - 270°) = cos(-180°)
• -cos(90° + 270°) = -cos 360°

☛ Also Check:

• sin 2 degrees
• sin 270 degrees
• sin 120 degrees
• sin 46 degrees
• sin 315 degrees
• sin 765 degrees

FAQs on Sin 270 Degrees

What is Sin 270 Degrees?

Sin 270 degrees is the value of sine trigonometric function for an angle equal to 270 degrees. The value of sin 270° is -1.

What is the Value of Sin 270° in Terms of Cosec 270°?

Since the cosecant function is the reciprocal of the sine function, we can write sin 270° as 1/cosec(270°). The value of cosec 270° is equal to -1.

How to Find the Value of Sin 270 Degrees?

The value of sin 270 degrees can be calculated by constructing an angle of 270° with the x-axis, and then finding the coordinates of the corresponding point (0, -1) on the unit circle. The value of sin 270° is equal to the y-coordinate (-1). ∴ sin 270° = -1.

What is the Value of Sin 270 Degrees in Terms of Cot 270°?

We can represent the sine function in terms of the cotangent function using trig identities, sin 270° can be written as -1/√(1 + cot²(270°)). Here, the value of cot 270° is equal to 0.

How to Find Sin 270° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 270° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(270°))
• ± tan 270°/√(1 + tan²(270°))
• ± 1/√(1 + cot²(270°))
• ± √(sec²(270°) - 1)/sec 270°
• 1/cosec 270°

☛ Also check: trigonometric table