Cos 47 Degrees

The value of cos 47 degrees is 0.6819983. . .. Cos 47 degrees in radians is written as cos (47° × π/180°), i.e., cos (0.820304. . .). In this article, we will discuss the methods to find the value of cos 47 degrees with examples.

• Cos 47°: 0.6819983. . .
• Cos (-47 degrees): 0.6819983. . .
• Cos 47° in radians: cos (0.8203047 . . .)

What is the Value of Cos 47 Degrees?

The value of cos 47 degrees in decimal is 0.681998360. . .. Cos 47 degrees can also be expressed using the equivalent of the given angle (47 degrees) in radians (0.82030 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 47 degrees = 47° × (π/180°) rad = 0.8203 . . .
∴ cos 47° = cos(0.8203) = 0.6819983. . .

Explanation:

For cos 47 degrees, the angle 47° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 47° value = 0.6819983. . .
Since the cosine function is a periodic function, we can represent cos 47° as, cos 47 degrees = cos(47° + n × 360°), n ∈ Z.
⇒ cos 47° = cos 407° = cos 767°, and so on.
Note: Since, cosine is an even function, the value of cos(-47°) = cos(47°).

Methods to Find Value of Cos 47 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 47° is given as 0.68199. . .. We can find the value of cos 47 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 47 Degrees Using Unit Circle

To find the value of cos 47 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 47° angle with the positive x-axis.
• The cos of 47 degrees equals the x-coordinate(0.682) of the point of intersection (0.682, 0.7314) of unit circle and r.

Hence the value of cos 47° = x = 0.682 (approx)

Cos 47° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 47 degrees as:

• ± √(1-sin²(47°))
• ± 1/√(1 + tan²(47°))
• ± cot 47°/√(1 + cot²(47°))
• ±√(cosec²(47°) - 1)/cosec 47°
• 1/sec 47°

Note: Since 47° lies in the 1st Quadrant, the final value of cos 47° will be positive.

We can use trigonometric identities to represent cos 47° as,

• -cos(180° - 47°) = -cos 133°
• -cos(180° + 47°) = -cos 227°
• sin(90° + 47°) = sin 137°
• sin(90° - 47°) = sin 43°

☛ Also Check:

• cos 37 degrees
• cos 36 degrees
• cos 20 degrees
• cos 930 degrees
• cos 115 degrees
• cos 77 degrees

FAQs on Cos 47 Degrees

What is Cos 47 Degrees?

Cos 47 degrees is the value of cosine trigonometric function for an angle equal to 47 degrees. The value of cos 47° is 0.682 (approx)

What is the Value of Cos 47 Degrees in Terms of Cot 47°?

We can represent the cosine function in terms of the cotangent function using trig identities, cos 47° can be written as cot 47°/√(1 + cot²(47°)). Here, the value of cot 47° is equal to 0.93251.

How to Find Cos 47° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 47° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(47°))
• ± 1/√(1 + tan²(47°))
• ± cot 47°/√(1 + cot²(47°))
• ± √(cosec²(47°) - 1)/cosec 47°
• 1/sec 47°

☛ Also check: trigonometric table

What is the Exact Value of cos 47 Degrees?

The exact value of cos 47 degrees can be given accurately up to 8 decimal places as 0.68199836.

How to Find the Value of Cos 47 Degrees?

The value of cos 47 degrees can be calculated by constructing an angle of 47° with the x-axis, and then finding the coordinates of the corresponding point (0.682, 0.7314) on the unit circle. The value of cos 47° is equal to the x-coordinate (0.682). ∴ cos 47° = 0.682.