Tan 47 Degrees

The value of tan 47 degrees is 1.0723687. . .. Tan 47 degrees in radians is written as tan (47° × π/180°), i.e., tan (0.820304. . .). In this article, we will discuss the methods to find the value of tan 47 degrees with examples.

• Tan 47° in decimal: 1.0723687. . .
• Tan (-47 degrees): -1.0723687. . .
• Tan 47° in radians: tan (0.8203047 . . .)

What is the Value of Tan 47 Degrees?

The value of tan 47 degrees in decimal is 1.072368710. . .. Tan 47 degrees can also be expressed using the equivalent of the given angle (47 degrees) in radians (0.82030 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 47 degrees = 47° × (π/180°) rad = 0.8203 . . .
∴ tan 47° = tan(0.8203) = 1.0723687. . .

Explanation:

For tan 47 degrees, the angle 47° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 47° value = 1.0723687. . .
Since the tangent function is a periodic function, we can represent tan 47° as, tan 47 degrees = tan(47° + n × 180°), n ∈ Z.
⇒ tan 47° = tan 227° = tan 407°, and so on.
Note: Since, tangent is an odd function, the value of tan(-47°) = -tan(47°).

Methods to Find Value of Tan 47 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 47° is given as 1.07236. . .. We can find the value of tan 47 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Tan 47° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 47 degrees as:

• sin(47°)/cos(47°)
• ± sin 47°/√(1 - sin²(47°))
• ± √(1 - cos²(47°))/cos 47°
• ± 1/√(cosec²(47°) - 1)
• ± √(sec²(47°) - 1)
• 1/cot 47°

Note: Since 47° lies in the 1st Quadrant, the final value of tan 47° will be positive.

We can use trigonometric identities to represent tan 47° as,

• cot(90° - 47°) = cot 43°
• -cot(90° + 47°) = -cot 137°
• -tan (180° - 47°) = -tan 133°

Tan 47 Degrees Using Unit Circle

To find the value of tan 47 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 47° angle with the positive x-axis.
• The tan of 47 degrees equals the y-coordinate(0.7314) divided by x-coordinate(0.682) of the point of intersection (0.682, 0.7314) of unit circle and r.

Hence the value of tan 47° = y/x = 1.0724 (approx).

☛ Also Check:

• tan 180 degrees
• tan 1 degrees
• tan 270 degrees
• tan 5 degrees
• tan 540 degrees
• tan 100 degrees

FAQs on Tan 47 Degrees

What is Tan 47 Degrees?

Tan 47 degrees is the value of tangent trigonometric function for an angle equal to 47 degrees. The value of tan 47° is 1.0724 (approx).

How to Find the Value of Tan 47 Degrees?

The value of tan 47 degrees can be calculated by constructing an angle of 47° with the x-axis, and then finding the coordinates of the corresponding point (0.682, 0.7314) on the unit circle. The value of tan 47° is equal to the y-coordinate(0.7314) divided by the x-coordinate (0.682). ∴ tan 47° = 1.0724

How to Find Tan 47° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 47° can be given in terms of other trigonometric functions as:

• sin(47°)/cos(47°)
• ± sin 47°/√(1 - sin²(47°))
• ± √(1 - cos²(47°))/cos 47°
• ± 1/√(cosec²(47°) - 1)
• ± √(sec²(47°) - 1)
• 1/cot 47°

☛ Also check: trigonometric table

What is the Value of Tan 47° in Terms of Sec 47°?

We can represent the tangent function in terms of the secant function using trig identities, tan 47° can be written as √(sec²(47°) - 1). Here, the value of sec 47° is equal to 1.4662.

What is the Value of Tan 47 Degrees in Terms of Sin 47°?

Using trigonometric identities, we can write tan 47° in terms of sin 47° as, tan(47°) = sin 47°/√(1 - sin²(47°)) . Here, the value of sin 47° is equal to 0.7314.