Cos 1 Degrees

The value of cos 1 degrees is 0.9998476. . .. Cos 1 degrees in radians is written as cos (1° × π/180°), i.e., cos (0.017453. . .). In this article, we will discuss the methods to find the value of cos 1 degrees with examples.

• Cos 1°: 0.9998476. . .
• Cos (-1 degrees): 0.9998476. . .
• Cos 1° in radians: cos (0.0174532 . . .)

What is the Value of Cos 1 Degrees?

The value of cos 1 degrees in decimal is 0.999847695. . .. Cos 1 degrees can also be expressed using the equivalent of the given angle (1 degrees) in radians (0.01745 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 1 degrees = 1° × (π/180°) rad = 0.0174 . . .
∴ cos 1° = cos(0.0174) = 0.9998476. . .

Explanation:

For cos 1 degrees, the angle 1° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 1° value = 0.9998476. . .
Since the cosine function is a periodic function, we can represent cos 1° as, cos 1 degrees = cos(1° + n × 360°), n ∈ Z.
⇒ cos 1° = cos 361° = cos 721°, and so on.
Note: Since, cosine is an even function, the value of cos(-1°) = cos(1°).

Methods to Find Value of Cos 1 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 1° is given as 0.99984. . .. We can find the value of cos 1 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 1 Degrees Using Unit Circle

To find the value of cos 1 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 1° angle with the positive x-axis.
• The cos of 1 degrees equals the x-coordinate(0.9998) of the point of intersection (0.9998, 0.0175) of unit circle and r.

Hence the value of cos 1° = x = 0.9998 (approx)

Cos 1° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 1 degrees as:

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

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

We can use trigonometric identities to represent cos 1° as,

• -cos(180° - 1°) = -cos 179°
• -cos(180° + 1°) = -cos 181°
• sin(90° + 1°) = sin 91°
• sin(90° - 1°) = sin 89°

☛ Also Check:

• cos 300 degrees
• cos 10 degrees
• cos 45 degrees
• cos 70 degrees
• cos 22 degrees
• cos 29 degrees

FAQs on Cos 1 Degrees

What is Cos 1 Degrees?

Cos 1 degrees is the value of cosine trigonometric function for an angle equal to 1 degrees. The value of cos 1° is 0.9998 (approx)

How to Find Cos 1° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 1° can be given in terms of other trigonometric functions as:

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

☛ Also check: trigonometry table

How to Find the Value of Cos 1 Degrees?

The value of cos 1 degrees can be calculated by constructing an angle of 1° with the x-axis, and then finding the coordinates of the corresponding point (0.9998, 0.0175) on the unit circle. The value of cos 1° is equal to the x-coordinate (0.9998). ∴ cos 1° = 0.9998.

What is the Exact Value of cos 1 Degrees?

The exact value of cos 1 degrees can be given accurately up to 8 decimal places as 0.99984769.

What is the Value of Cos 1 Degrees in Terms of Tan 1°?

We know, using trig identities, we can write cos 1° as 1/√(1 + tan²(1°)). Here, the value of tan 1° is equal to 0.017455.