Tan 49 Degrees
The value of tan 49 degrees is 1.1503684. . .. Tan 49 degrees in radians is written as tan (49° × π/180°), i.e., tan (0.855211. . .). In this article, we will discuss the methods to find the value of tan 49 degrees with examples.
- Tan 49° in decimal: 1.1503684. . .
- Tan (-49 degrees): -1.1503684. . .
- Tan 49° in radians: tan (0.8552113 . . .)
What is the Value of Tan 49 Degrees?
The value of tan 49 degrees in decimal is 1.150368407. . .. Tan 49 degrees can also be expressed using the equivalent of the given angle (49 degrees) in radians (0.85521 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 49 degrees = 49° × (π/180°) rad = 0.8552 . . .
∴ tan 49° = tan(0.8552) = 1.1503684. . .
Explanation:
For tan 49 degrees, the angle 49° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 49° value = 1.1503684. . .
Since the tangent function is a periodic function, we can represent tan 49° as, tan 49 degrees = tan(49° + n × 180°), n ∈ Z.
⇒ tan 49° = tan 229° = tan 409°, and so on.
Note: Since, tangent is an odd function, the value of tan(-49°) = -tan(49°).
Methods to Find Value of Tan 49 Degrees
The tangent function is positive in the 1st quadrant. The value of tan 49° is given as 1.15036. . .. We can find the value of tan 49 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Tan 49° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 49 degrees as:
- sin(49°)/cos(49°)
- ± sin 49°/√(1 - sin²(49°))
- ± √(1 - cos²(49°))/cos 49°
- ± 1/√(cosec²(49°) - 1)
- ± √(sec²(49°) - 1)
- 1/cot 49°
Note: Since 49° lies in the 1st Quadrant, the final value of tan 49° will be positive.
We can use trigonometric identities to represent tan 49° as,
- cot(90° - 49°) = cot 41°
- -cot(90° + 49°) = -cot 139°
- -tan (180° - 49°) = -tan 131°
Tan 49 Degrees Using Unit Circle
To find the value of tan 49 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 49° angle with the positive x-axis.
- The tan of 49 degrees equals the y-coordinate(0.7547) divided by x-coordinate(0.6561) of the point of intersection (0.6561, 0.7547) of unit circle and r.
Hence the value of tan 49° = y/x = 1.1504 (approx).
☛ Also Check:
FAQs on Tan 49 Degrees
What is Tan 49 Degrees?
Tan 49 degrees is the value of tangent trigonometric function for an angle equal to 49 degrees. The value of tan 49° is 1.1504 (approx).
How to Find Tan 49° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 49° can be given in terms of other trigonometric functions as:
- sin(49°)/cos(49°)
- ± sin 49°/√(1 - sin²(49°))
- ± √(1 - cos²(49°))/cos 49°
- ± 1/√(cosec²(49°) - 1)
- ± √(sec²(49°) - 1)
- 1/cot 49°
☛ Also check: trigonometric table
What is the Value of Tan 49 Degrees in Terms of Sin 49°?
Using trigonometric identities, we can write tan 49° in terms of sin 49° as, tan(49°) = sin 49°/√(1 - sin²(49°)) . Here, the value of sin 49° is equal to 0.7547.
How to Find the Value of Tan 49 Degrees?
The value of tan 49 degrees can be calculated by constructing an angle of 49° with the x-axis, and then finding the coordinates of the corresponding point (0.6561, 0.7547) on the unit circle. The value of tan 49° is equal to the y-coordinate(0.7547) divided by the x-coordinate (0.6561). ∴ tan 49° = 1.1504
What is the Value of Tan 49° in Terms of Cosec 49°?
Since the tangent function can be represented using the cosecant function, we can write tan 49° as 1/√(cosec²(49°) - 1). The value of cosec 49° is equal to 1.32501.