Tan 50 Degrees

The value of tan 50 degrees is 1.1917535. . .. Tan 50 degrees in radians is written as tan (50° × π/180°), i.e., tan (5π/18) or tan (0.872664. . .). In this article, we will discuss the methods to find the value of tan 50 degrees with examples.

• Tan 50° in decimal: 1.1917535. . .
• Tan (-50 degrees): -1.1917535. . .
• Tan 50° in radians: tan (5π/18) or tan (0.8726646 . . .)

What is the Value of Tan 50 Degrees?

The value of tan 50 degrees in decimal is 1.191753592. . .. Tan 50 degrees can also be expressed using the equivalent of the given angle (50 degrees) in radians (0.87266 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 50 degrees = 50° × (π/180°) rad = 5π/18 or 0.8726 . . .
∴ tan 50° = tan(0.8726) = 1.1917535. . .

Explanation:

For tan 50 degrees, the angle 50° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 50° value = 1.1917535. . .
Since the tangent function is a periodic function, we can represent tan 50° as, tan 50 degrees = tan(50° + n × 180°), n ∈ Z.
⇒ tan 50° = tan 230° = tan 410°, and so on.
Note: Since, tangent is an odd function, the value of tan(-50°) = -tan(50°).

Methods to Find Value of Tan 50 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 50° is given as 1.19175. . .. We can find the value of tan 50 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Tan 50 Degrees Using Unit Circle

To find the value of tan 50 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 50° angle with the positive x-axis.
• The tan of 50 degrees equals the y-coordinate(0.766) divided by x-coordinate(0.6428) of the point of intersection (0.6428, 0.766) of unit circle and r.

Hence the value of tan 50° = y/x = 1.1918 (approx).

Tan 50° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 50 degrees as:

• sin(50°)/cos(50°)
• ± sin 50°/√(1 - sin²(50°))
• ± √(1 - cos²(50°))/cos 50°
• ± 1/√(cosec²(50°) - 1)
• ± √(sec²(50°) - 1)
• 1/cot 50°

Note: Since 50° lies in the 1st Quadrant, the final value of tan 50° will be positive.

We can use trigonometric identities to represent tan 50° as,

• cot(90° - 50°) = cot 40°
• -cot(90° + 50°) = -cot 140°
• -tan (180° - 50°) = -tan 130°

☛ Also Check:

• tan 225 degrees
• tan 0 degrees
• tan 150 degrees
• tan 240 degrees
• tan 44 degrees
• tan 480 degrees

FAQs on Tan 50 Degrees

What is Tan 50 Degrees?

Tan 50 degrees is the value of tangent trigonometric function for an angle equal to 50 degrees. The value of tan 50° is 1.1918 (approx).

What is the Value of Tan 50° in Terms of Sec 50°?

We can represent the tangent function in terms of the secant function using trig identities, tan 50° can be written as √(sec²(50°) - 1). Here, the value of sec 50° is equal to 1.5557.

How to Find Tan 50° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 50° can be given in terms of other trigonometric functions as:

• sin(50°)/cos(50°)
• ± sin 50°/√(1 - sin²(50°))
• ± √(1 - cos²(50°))/cos 50°
• ± 1/√(cosec²(50°) - 1)
• ± √(sec²(50°) - 1)
• 1/cot 50°

☛ Also check: trigonometric table

How to Find the Value of Tan 50 Degrees?

The value of tan 50 degrees can be calculated by constructing an angle of 50° with the x-axis, and then finding the coordinates of the corresponding point (0.6428, 0.766) on the unit circle. The value of tan 50° is equal to the y-coordinate(0.766) divided by the x-coordinate (0.6428). ∴ tan 50° = 1.1918

What is the Value of Tan 50 Degrees in Terms of Cos 50°?

We know, using trig identities, we can write tan 50° as √(1 - cos²(50°))/cos 50°. Here, the value of cos 50° is equal to 0.642787.