Sin 59 Degrees

The value of sin 59 degrees is 0.8571673. . .. Sin 59 degrees in radians is written as sin (59° × π/180°), i.e., sin (1.029744. . .). In this article, we will discuss the methods to find the value of sin 59 degrees with examples.

• Sin 59°: 0.8571673. . .
• Sin (-59 degrees): -0.8571673. . .
• Sin 59° in radians: sin (1.0297442 . . .)

What is the Value of Sin 59 Degrees?

The value of sin 59 degrees in decimal is 0.857167300. . .. Sin 59 degrees can also be expressed using the equivalent of the given angle (59 degrees) in radians (1.02974 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 59 degrees = 59° × (π/180°) rad = 1.0297 . . .
∴ sin 59° = sin(1.0297) = 0.8571673. . .

Explanation:

For sin 59 degrees, the angle 59° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 59° value = 0.8571673. . .
Since the sine function is a periodic function, we can represent sin 59° as, sin 59 degrees = sin(59° + n × 360°), n ∈ Z.
⇒ sin 59° = sin 419° = sin 779°, and so on.
Note: Since, sine is an odd function, the value of sin(-59°) = -sin(59°).

Methods to Find Value of Sin 59 Degrees

The sine function is positive in the 1st quadrant. The value of sin 59° is given as 0.85716. . .. We can find the value of sin 59 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 59° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 59 degrees as:

• ± √(1-cos²(59°))
• ± tan 59°/√(1 + tan²(59°))
• ± 1/√(1 + cot²(59°))
• ± √(sec²(59°) - 1)/sec 59°
• 1/cosec 59°

Note: Since 59° lies in the 1st Quadrant, the final value of sin 59° will be positive.

We can use trigonometric identities to represent sin 59° as,

• sin(180° - 59°) = sin 121°
• -sin(180° + 59°) = -sin 239°
• cos(90° - 59°) = cos 31°
• -cos(90° + 59°) = -cos 149°

Sin 59 Degrees Using Unit Circle

To find the value of sin 59 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 59° angle with the positive x-axis.
• The sin of 59 degrees equals the y-coordinate(0.8572) of the point of intersection (0.515, 0.8572) of unit circle and r.

Hence the value of sin 59° = y = 0.8572 (approx)

☛ Also Check:

• sin 13 degrees
• sin 556 degrees
• sin 40 degrees
• sin 59 degrees
• sin 510 degrees
• sin 115 degrees

FAQs on Sin 59 Degrees

What is Sin 59 Degrees?

Sin 59 degrees is the value of sine trigonometric function for an angle equal to 59 degrees. The value of sin 59° is 0.8572 (approx).

How to Find the Value of Sin 59 Degrees?

The value of sin 59 degrees can be calculated by constructing an angle of 59° with the x-axis, and then finding the coordinates of the corresponding point (0.515, 0.8572) on the unit circle. The value of sin 59° is equal to the y-coordinate (0.8572). ∴ sin 59° = 0.8572.

What is the Value of Sin 59 Degrees in Terms of Cot 59°?

We can represent the sine function in terms of the cotangent function using trig identities, sin 59° can be written as 1/√(1 + cot²(59°)). Here, the value of cot 59° is equal to 0.60086.

How to Find Sin 59° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 59° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(59°))
• ± tan 59°/√(1 + tan²(59°))
• ± 1/√(1 + cot²(59°))
• ± √(sec²(59°) - 1)/sec 59°
• 1/cosec 59°

☛ Also check: trigonometry table

What is the Exact Value of sin 59 Degrees?

The exact value of sin 59 degrees can be given accurately up to 8 decimal places as 0.85716730.