Cos 71 Degrees

The value of cos 71 degrees is 0.3255681. . .. Cos 71 degrees in radians is written as cos (71° × π/180°), i.e., cos (1.239183. . .). In this article, we will discuss the methods to find the value of cos 71 degrees with examples.

• Cos 71°: 0.3255681. . .
• Cos (-71 degrees): 0.3255681. . .
• Cos 71° in radians: cos (1.2391837 . . .)

What is the Value of Cos 71 Degrees?

The value of cos 71 degrees in decimal is 0.325568154. . .. Cos 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 . . .
∴ cos 71° = cos(1.2391) = 0.3255681. . .

Explanation:

For cos 71 degrees, the angle 71° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 71° value = 0.3255681. . .
Since the cosine function is a periodic function, we can represent cos 71° as, cos 71 degrees = cos(71° + n × 360°), n ∈ Z.
⇒ cos 71° = cos 431° = cos 791°, and so on.
Note: Since, cosine is an even function, the value of cos(-71°) = cos(71°).

Methods to Find Value of Cos 71 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 71° is given as 0.32556. . .. We can find the value of cos 71 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 71 Degrees Using Unit Circle

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

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

Hence the value of cos 71° = x = 0.3256 (approx)

Cos 71° in Terms of Trigonometric Functions

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

• ± √(1-sin²(71°))
• ± 1/√(1 + tan²(71°))
• ± cot 71°/√(1 + cot²(71°))
• ±√(cosec²(71°) - 1)/cosec 71°
• 1/sec 71°

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

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

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

☛ Also Check:

• cos 225 degrees
• cos 270 degrees
• cos 75 degrees
• cos 34 degrees
• cos 125 degrees
• cos 900 degrees

FAQs on Cos 71 Degrees

What is Cos 71 Degrees?

Cos 71 degrees is the value of cosine trigonometric function for an angle equal to 71 degrees. The value of cos 71° is 0.3256 (approx)

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

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

• ± √(1-sin²(71°))
• ± 1/√(1 + tan²(71°))
• ± cot 71°/√(1 + cot²(71°))
• ± √(cosec²(71°) - 1)/cosec 71°
• 1/sec 71°

☛ Also check: trigonometry table

What is the Exact Value of cos 71 Degrees?

The exact value of cos 71 degrees can be given accurately up to 8 decimal places as 0.32556815.

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

Using trigonometric identities, we can write cos 71° in terms of sin 71° as, cos(71°) = √(1 - sin²(71°)). Here, the value of sin 71° is equal to 0.9455.

How to Find the Value of Cos 71 Degrees?

The value of cos 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 cos 71° is equal to the x-coordinate (0.3256). ∴ cos 71° = 0.3256.