Tan 37 Degrees

The value of tan 37 degrees is 0.7535540. . .. Tan 37 degrees in radians is written as tan (37° × π/180°), i.e., tan (0.645771. . .). In this article, we will discuss the methods to find the value of tan 37 degrees with examples.

• Tan 37° in decimal: 0.7535540. . .
• Tan (-37 degrees): -0.7535540. . .
• Tan 37° in radians: tan (0.6457718 . . .)

What is the Value of Tan 37 Degrees?

The value of tan 37 degrees in decimal is 0.753554050. . .. Tan 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 . . .
∴ tan 37° = tan(0.6457) = 0.7535540. . .

Explanation:

For tan 37 degrees, the angle 37° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 37° value = 0.7535540. . .
Since the tangent function is a periodic function, we can represent tan 37° as, tan 37 degrees = tan(37° + n × 180°), n ∈ Z.
⇒ tan 37° = tan 217° = tan 397°, and so on.
Note: Since, tangent is an odd function, the value of tan(-37°) = -tan(37°).

Methods to Find Value of Tan 37 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 37° is given as 0.75355. . .. We can find the value of tan 37 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Tan 37° in Terms of Trigonometric Functions

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

• sin(37°)/cos(37°)
• ± sin 37°/√(1 - sin²(37°))
• ± √(1 - cos²(37°))/cos 37°
• ± 1/√(cosec²(37°) - 1)
• ± √(sec²(37°) - 1)
• 1/cot 37°

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

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

• cot(90° - 37°) = cot 53°
• -cot(90° + 37°) = -cot 127°
• -tan (180° - 37°) = -tan 143°

Tan 37 Degrees Using Unit Circle

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

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

Hence the value of tan 37° = y/x = 0.7536 (approx).

☛ Also Check:

• tan 20 degrees
• tan 40 degrees
• tan 10 degrees
• tan 390 degrees
• tan 28 degrees
• tan 89 degrees

FAQs on Tan 37 Degrees

What is Tan 37 Degrees?

Tan 37 degrees is the value of tangent trigonometric function for an angle equal to 37 degrees. The value of tan 37° is 0.7536 (approx).

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

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

• sin(37°)/cos(37°)
• ± sin 37°/√(1 - sin²(37°))
• ± √(1 - cos²(37°))/cos 37°
• ± 1/√(cosec²(37°) - 1)
• ± √(sec²(37°) - 1)
• 1/cot 37°

☛ Also check: trigonometric table

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

We know, using trig identities, we can write tan 37° as √(1 - cos²(37°))/cos 37°. Here, the value of cos 37° is equal to 0.798635.

How to Find the Value of Tan 37 Degrees?

The value of tan 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 tan 37° is equal to the y-coordinate(0.6018) divided by the x-coordinate (0.7986). ∴ tan 37° = 0.7536

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

We can represent the tangent function in terms of the secant function using trig identities, tan 37° can be written as √(sec²(37°) - 1). Here, the value of sec 37° is equal to 1.2521.