Sin 71 Degrees

The value of sin 71 degrees is 0.9455185. . .. Sin 71 degrees in radians is written as sin (71° × π/180°), i.e., sin (1.239183. . .). In this article, we will discuss the methods to find the value of sin 71 degrees with examples.

• Sin 71°: 0.9455185. . .
• Sin (-71 degrees): -0.9455185. . .
• Sin 71° in radians: sin (1.2391837 . . .)

What is the Value of Sin 71 Degrees?

The value of sin 71 degrees in decimal is 0.945518575. . .. Sin 71 degrees can also be expressed using the equivalent of the given angle (71 degrees) in radians (1.23918 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 71 degrees = 71° × (π/180°) rad = 1.2391 . . .
∴ sin 71° = sin(1.2391) = 0.9455185. . .

Explanation:

For sin 71 degrees, the angle 71° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 71° value = 0.9455185. . .
Since the sine function is a periodic function, we can represent sin 71° as, sin 71 degrees = sin(71° + n × 360°), n ∈ Z.
⇒ sin 71° = sin 431° = sin 791°, and so on.
Note: Since, sine is an odd function, the value of sin(-71°) = -sin(71°).

Methods to Find Value of Sin 71 Degrees

The sine function is positive in the 1st quadrant. The value of sin 71° is given as 0.94551. . .. We can find the value of sin 71 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 71° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 71 degrees as:

• ± √(1-cos²(71°))
• ± tan 71°/√(1 + tan²(71°))
• ± 1/√(1 + cot²(71°))
• ± √(sec²(71°) - 1)/sec 71°
• 1/cosec 71°

Note: Since 71° lies in the 1st Quadrant, the final value of sin 71° will be positive.

We can use trigonometric identities to represent sin 71° as,

• sin(180° - 71°) = sin 109°
• -sin(180° + 71°) = -sin 251°
• cos(90° - 71°) = cos 19°
• -cos(90° + 71°) = -cos 161°

Sin 71 Degrees Using Unit Circle

To find the value of sin 71 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 71° angle with the positive x-axis.
• The sin of 71 degrees equals the y-coordinate(0.9455) of the point of intersection (0.3256, 0.9455) of unit circle and r.

Hence the value of sin 71° = y = 0.9455 (approx)

☛ Also Check:

• sin 10 degrees
• sin 135 degrees
• sin 40 degrees
• sin 85 degrees
• sin 836 degrees
• sin 33 degrees

FAQs on Sin 71 Degrees

What is Sin 71 Degrees?

Sin 71 degrees is the value of sine trigonometric function for an angle equal to 71 degrees. The value of sin 71° is 0.9455 (approx).

How to Find the Value of Sin 71 Degrees?

The value of sin 71 degrees can be calculated by constructing an angle of 71° with the x-axis, and then finding the coordinates of the corresponding point (0.3256, 0.9455) on the unit circle. The value of sin 71° is equal to the y-coordinate (0.9455). ∴ sin 71° = 0.9455.

What is the Value of Sin 71 Degrees in Terms of Cos 71°?

Using trigonometric identities, we can write sin 71° in terms of cos 71° as, sin(71°) = √(1-cos²(71°)). Here, the value of cos 71° is equal to 0.3255681.

How to Find Sin 71° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 71° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(71°))
• ± tan 71°/√(1 + tan²(71°))
• ± 1/√(1 + cot²(71°))
• ± √(sec²(71°) - 1)/sec 71°
• 1/cosec 71°

☛ Also check: trigonometry table

What is the Exact Value of sin 71 Degrees?

The exact value of sin 71 degrees can be given accurately up to 8 decimal places as 0.94551857.