Cos 40 Degrees

The value of cos 40 degrees is 0.7660444. . .. Cos 40 degrees in radians is written as cos (40° × π/180°), i.e., cos (2π/9) or cos (0.698131. . .). In this article, we will discuss the methods to find the value of cos 40 degrees with examples.

• Cos 40°: 0.7660444. . .
• Cos (-40 degrees): 0.7660444. . .
• Cos 40° in radians: cos (2π/9) or cos (0.6981317 . . .)

What is the Value of Cos 40 Degrees?

The value of cos 40 degrees in decimal is 0.766044443. . .. Cos 40 degrees can also be expressed using the equivalent of the given angle (40 degrees) in radians (0.69813 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 40 degrees = 40° × (π/180°) rad = 2π/9 or 0.6981 . . .
∴ cos 40° = cos(0.6981) = 0.7660444. . .

Explanation:

For cos 40 degrees, the angle 40° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 40° value = 0.7660444. . .
Since the cosine function is a periodic function, we can represent cos 40° as, cos 40 degrees = cos(40° + n × 360°), n ∈ Z.
⇒ cos 40° = cos 400° = cos 760°, and so on.
Note: Since, cosine is an even function, the value of cos(-40°) = cos(40°).

Methods to Find Value of Cos 40 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 40° is given as 0.76604. . .. We can find the value of cos 40 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 40 Degrees Using Unit Circle

To find the value of cos 40 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 40° angle with the positive x-axis.
• The cos of 40 degrees equals the x-coordinate(0.766) of the point of intersection (0.766, 0.6428) of unit circle and r.

Hence the value of cos 40° = x = 0.766 (approx)

Cos 40° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 40 degrees as:

• ± √(1-sin²(40°))
• ± 1/√(1 + tan²(40°))
• ± cot 40°/√(1 + cot²(40°))
• ±√(cosec²(40°) - 1)/cosec 40°
• 1/sec 40°

Note: Since 40° lies in the 1st Quadrant, the final value of cos 40° will be positive.

We can use trigonometric identities to represent cos 40° as,

• -cos(180° - 40°) = -cos 140°
• -cos(180° + 40°) = -cos 220°
• sin(90° + 40°) = sin 130°
• sin(90° - 40°) = sin 50°

☛ Also Check:

• cos 21 degrees
• cos 36 degrees
• cos 2 degrees
• cos 33 degrees
• cos 245 degrees
• cos 83 degrees

FAQs on Cos 40 Degrees

What is Cos 40 Degrees?

Cos 40 degrees is the value of cosine trigonometric function for an angle equal to 40 degrees. The value of cos 40° is 0.766 (approx)

What is the Value of Cos 40° in Terms of Cosec 40°?

Since the cosine function can be represented using the cosecant function, we can write cos 40° as [√(cosec²(40°) - 1)/cosec 40°]. The value of cosec 40° is equal to 1.55572.

What is the Value of Cos 40 Degrees in Terms of Cot 40°?

We can represent the cosine function in terms of the cotangent function using trig identities, cos 40° can be written as cot 40°/√(1 + cot²(40°)). Here, the value of cot 40° is equal to 1.19175.

How to Find Cos 40° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 40° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(40°))
• ± 1/√(1 + tan²(40°))
• ± cot 40°/√(1 + cot²(40°))
• ± √(cosec²(40°) - 1)/cosec 40°
• 1/sec 40°

☛ Also check: trigonometry table

How to Find the Value of Cos 40 Degrees?

The value of cos 40 degrees can be calculated by constructing an angle of 40° with the x-axis, and then finding the coordinates of the corresponding point (0.766, 0.6428) on the unit circle. The value of cos 40° is equal to the x-coordinate (0.766). ∴ cos 40° = 0.766.