Cos 37 Degrees

The value of cos 37 degrees is 0.7986355. . .. Cos 37 degrees in radians is written as cos (37° × π/180°), i.e., cos (0.645771. . .). In this article, we will discuss the methods to find the value of cos 37 degrees with examples.

• Cos 37°: 0.7986355. . .
• Cos (-37 degrees): 0.7986355. . .
• Cos 37° in radians: cos (0.6457718 . . .)

What is the Value of Cos 37 Degrees?

The value of cos 37 degrees in decimal is 0.798635510. . .. Cos 37 degrees can also be expressed using the equivalent of the given angle (37 degrees) in radians (0.64577 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 37 degrees = 37° × (π/180°) rad = 0.6457 . . .
∴ cos 37° = cos(0.6457) = 0.7986355. . .

Explanation:

For cos 37 degrees, the angle 37° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 37° value = 0.7986355. . .
Since the cosine function is a periodic function, we can represent cos 37° as, cos 37 degrees = cos(37° + n × 360°), n ∈ Z.
⇒ cos 37° = cos 397° = cos 757°, and so on.
Note: Since, cosine is an even function, the value of cos(-37°) = cos(37°).

Methods to Find Value of Cos 37 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 37° is given as 0.79863. . .. We can find the value of cos 37 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 37° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 37 degrees as:

• ± √(1-sin²(37°))
• ± 1/√(1 + tan²(37°))
• ± cot 37°/√(1 + cot²(37°))
• ±√(cosec²(37°) - 1)/cosec 37°
• 1/sec 37°

Note: Since 37° lies in the 1st Quadrant, the final value of cos 37° will be positive.

We can use trigonometric identities to represent cos 37° as,

• -cos(180° - 37°) = -cos 143°
• -cos(180° + 37°) = -cos 217°
• sin(90° + 37°) = sin 127°
• sin(90° - 37°) = sin 53°

Cos 37 Degrees Using Unit Circle

To find the value of cos 37 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 37° angle with the positive x-axis.
• The cos of 37 degrees equals the x-coordinate(0.7986) of the point of intersection (0.7986, 0.6018) of unit circle and r.

Hence the value of cos 37° = x = 0.7986 (approx)

☛ Also Check:

• cos 240 degrees
• cos 30 degrees
• cos 120 degrees
• cos 720 degrees
• cos 80 degrees
• cos 1140 degrees

FAQs on Cos 37 Degrees

What is Cos 37 Degrees?

Cos 37 degrees is the value of cosine trigonometric function for an angle equal to 37 degrees. The value of cos 37° is 0.7986 (approx)

How to Find the Value of Cos 37 Degrees?

The value of cos 37 degrees can be calculated by constructing an angle of 37° with the x-axis, and then finding the coordinates of the corresponding point (0.7986, 0.6018) on the unit circle. The value of cos 37° is equal to the x-coordinate (0.7986). ∴ cos 37° = 0.7986.

What is the Value of Cos 37 Degrees in Terms of Tan 37°?

We know, using trig identities, we can write cos 37° as 1/√(1 + tan²(37°)). Here, the value of tan 37° is equal to 0.753554.

How to Find Cos 37° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 37° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(37°))
• ± 1/√(1 + tan²(37°))
• ± cot 37°/√(1 + cot²(37°))
• ± √(cosec²(37°) - 1)/cosec 37°
• 1/sec 37°

☛ Also check: trigonometry table

What is the Value of Cos 37° in Terms of Sec 37°?

Since the secant function is the reciprocal of the cosine function, we can write cos 37° as 1/sec(37°). The value of sec 37° is equal to 1.252135.