Как найти sin 450

The value of sin 450 degrees is 1. Sin 450 degrees in radians is written as sin (450° × π/180°), i.e., sin (5π/2) or sin (7.853981. . .). In this article, we will discuss the methods to find the value of sin 450 degrees with examples.

• Sin 450°: 1
• Sin (-450 degrees): -1
• Sin 450° in radians: sin (5π/2) or sin (7.8539816 . . .)

What is the Value of Sin 450 Degrees?

The value of sin 450 degrees is 1. Sin 450 degrees can also be expressed using the equivalent of the given angle (450 degrees) in radians (7.85398 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 450 degrees = 450° × (π/180°) rad = 5π/2 or 7.8539 . . .
∴ sin 450° = sin(7.8539) = 1

Explanation:

For sin 450°, the angle 450° > 360°. Given the periodic property of the sine function, we can represent it as sin(450° mod 360°) = sin(90°). The angle 450°, coterminal to angle 90°, lies on the positive y-axis.
Thus, sin 450 degrees value = 1
Similarly, sin 450° can also be written as, sin 450 degrees = (450° + n × 360°), n ∈ Z.
⇒ sin 450° = sin 810° = sin 1170°, and so on.
Note: Since, sine is an odd function, the value of sin(-450°) = -sin(450°).

Methods to Find Value of Sin 450 Degrees

The value of sin 450° is given as 1. We can find the value of sin 450 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 450° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 450 degrees as:

• ± √(1-cos²(450°))
• ± tan 450°/√(1 + tan²(450°))
• ± 1/√(1 + cot²(450°))
• ± √(sec²(450°) – 1)/sec 450°
• 1/cosec 450°

Note: Since 450° lies on the positive y-axis, the final value of sin 450° will be positive.

We can use trigonometric identities to represent sin 450° as,

• sin(180° – 450°) = sin(-270°)
• -sin(180° + 450°) = -sin 630°
• cos(90° – 450°) = cos(-360°)
• -cos(90° + 450°) = -cos 540°

Sin 450 Degrees Using Unit Circle

To find the value of sin 450 degrees using the unit circle, represent 450° in the form (1 × 360°) + 90° [∵ 450°>360°] ∵ sine is a periodic function, sin 450° = sin 90°.

• Rotate ‘r’ anticlockwise to form a 90° or 450° angle with the positive x-axis.
• The sin of 450 degrees equals the y-coordinate(1) of the point of intersection (0, 1) of unit circle and r.

Hence the value of sin 450° = y = 1

☛ Also Check:

• sin 20 degrees
• sin 180 degrees
• sin 135 degrees
• sin 656 degrees
• sin 130 degrees
• sin 315 degrees

FAQs on Sin 450 Degrees

What is Sin 450 Degrees?

Sin 450 degrees is the value of sine trigonometric function for an angle equal to 450 degrees. The value of sin 450° is 1.

What is the Value of Sin 450° in Terms of Cosec 450°?

Since the sine function can be represented using the cosecant function, we can write sin 450° as 1/cosec 450°. The value of cosec 450° is equal to 1.

How to Find the Value of Sin 450 Degrees?

The value of sin 450 degrees can be calculated by constructing an angle of 450° with the x-axis, and then finding the coordinates of the corresponding point (0, 1) on the unit circle. The value of sin 450° is equal to the y-coordinate (1). ∴ sin 450° = 1.

What is the Value of Sin 450 Degrees in Terms of Cos 450°?

Using trigonometric identities, we can write sin 450° in terms of cos 450° as, sin(450°) = √(1-cos²(450°)). Here, the value of cos 450° is equal to 0.

How to Find Sin 450° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 450° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(450°))
• ± tan 450°/√(1 + tan²(450°))
• ± 1/√(1 + cot²(450°))
• ± √(sec²(450°) – 1)/sec 450°
• 1/cosec 450°

☛ Also check: trigonometric table