A day full of math games & activities. Find one near you.

Cos 51 Degrees

The value of cos 51 degrees is 0.6293203. . .. Cos 51 degrees in radians is written as cos (51° × π/180°), i.e., cos (17π/60) or cos (0.890117. . .). In this article, we will discuss the methods to find the value of cos 51 degrees with examples.

Cos 51°: 0.6293203. . .
Cos (-51 degrees): 0.6293203. . .
Cos 51° in radians: cos (17π/60) or cos (0.8901179 . . .)

What is the Value of Cos 51 Degrees?

The value of cos 51 degrees in decimal is 0.629320391. . .. Cos 51 degrees can also be expressed using the equivalent of the given angle (51 degrees) in radians (0.89011 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 51 degrees = 51° × (π/180°) rad = 17π/60 or 0.8901 . . .
∴ cos 51° = cos(0.8901) = 0.6293203. . .

Explanation:

For cos 51 degrees, the angle 51° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 51° value = 0.6293203. . .
Since the cosine function is a periodic function, we can represent cos 51° as, cos 51 degrees = cos(51° + n × 360°), n ∈ Z.
⇒ cos 51° = cos 411° = cos 771°, and so on.
Note: Since, cosine is an even function, the value of cos(-51°) = cos(51°).

Methods to Find Value of Cos 51 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 51° is given as 0.62932. . .. We can find the value of cos 51 degrees by:

Using Unit Circle
Using Trigonometric Functions

Cos 51 Degrees Using Unit Circle

To find the value of cos 51 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 51° angle with the positive x-axis.
The cos of 51 degrees equals the x-coordinate(0.6293) of the point of intersection (0.6293, 0.7771) of unit circle and r.

Hence the value of cos 51° = x = 0.6293 (approx)

Cos 51° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 51 degrees as:

± √(1-sin²(51°))
± 1/√(1 + tan²(51°))
± cot 51°/√(1 + cot²(51°))
±√(cosec²(51°) - 1)/cosec 51°
1/sec 51°

Note: Since 51° lies in the 1st Quadrant, the final value of cos 51° will be positive.

We can use trigonometric identities to represent cos 51° as,

-cos(180° - 51°) = -cos 129°
-cos(180° + 51°) = -cos 231°
sin(90° + 51°) = sin 141°
sin(90° - 51°) = sin 39°

☛ Also Check:

Examples Using Cos 51 Degrees

Example 1: Using the value of cos 51°, solve: (1-sin²(51°)).

Solution:
We know, (1-sin²(51°)) = (cos²(51°)) = 0.396
⇒ (1-sin²(51°)) = 0.396
Example 2: Simplify: 3 (cos 51°/sin 141°)

Solution:

We know cos 51° = sin 141°
⇒ 3 cos 51°/sin 141° = 3 (cos 51°/cos 51°)
= 3(1) = 3
Example 3: Find the value of 2 cos(51°)/3 sin(39°).

Solution:

Using trigonometric identities, we know, cos(51°) = sin(90° - 51°) = sin 39°.
⇒ cos(51°) = sin(39°)
⇒ Value of 2 cos(51°)/3 sin(39°) = 2/3

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on Cos 51 Degrees

What is Cos 51 Degrees?

Cos 51 degrees is the value of cosine trigonometric function for an angle equal to 51 degrees. The value of cos 51° is 0.6293 (approx)

How to Find Cos 51° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 51° can be given in terms of other trigonometric functions as:

± √(1-sin²(51°))
± 1/√(1 + tan²(51°))
± cot 51°/√(1 + cot²(51°))
± √(cosec²(51°) - 1)/cosec 51°
1/sec 51°

☛ Also check: trigonometry table

What is the Value of Cos 51 Degrees in Terms of Cot 51°?

We can represent the cosine function in terms of the cotangent function using trig identities, cos 51° can be written as cot 51°/√(1 + cot²(51°)). Here, the value of cot 51° is equal to 0.80978.

What is the Exact Value of cos 51 Degrees?

The exact value of cos 51 degrees can be given accurately up to 8 decimal places as 0.62932039.

How to Find the Value of Cos 51 Degrees?

The value of cos 51 degrees can be calculated by constructing an angle of 51° with the x-axis, and then finding the coordinates of the corresponding point (0.6293, 0.7771) on the unit circle. The value of cos 51° is equal to the x-coordinate (0.6293). ∴ cos 51° = 0.6293.

Download FREE Study Materials

Trigonometry

Math worksheets and
visual curriculum