Tan 46 Degrees
The value of tan 46 degrees is 1.0355303. . .. Tan 46 degrees in radians is written as tan (46° × π/180°), i.e., tan (23π/90) or tan (0.802851. . .). In this article, we will discuss the methods to find the value of tan 46 degrees with examples.
- Tan 46° in decimal: 1.0355303. . .
- Tan (-46 degrees): -1.0355303. . .
- Tan 46° in radians: tan (23π/90) or tan (0.8028514 . . .)
What is the Value of Tan 46 Degrees?
The value of tan 46 degrees in decimal is 1.035530313. . .. Tan 46 degrees can also be expressed using the equivalent of the given angle (46 degrees) in radians (0.80285 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 46 degrees = 46° × (π/180°) rad = 23π/90 or 0.8028 . . .
∴ tan 46° = tan(0.8028) = 1.0355303. . .
Explanation:
For tan 46 degrees, the angle 46° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 46° value = 1.0355303. . .
Since the tangent function is a periodic function, we can represent tan 46° as, tan 46 degrees = tan(46° + n × 180°), n ∈ Z.
⇒ tan 46° = tan 226° = tan 406°, and so on.
Note: Since, tangent is an odd function, the value of tan(-46°) = -tan(46°).
Methods to Find Value of Tan 46 Degrees
The tangent function is positive in the 1st quadrant. The value of tan 46° is given as 1.03553. . .. We can find the value of tan 46 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Tan 46 Degrees Using Unit Circle
To find the value of tan 46 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 46° angle with the positive x-axis.
- The tan of 46 degrees equals the y-coordinate(0.7193) divided by x-coordinate(0.6947) of the point of intersection (0.6947, 0.7193) of unit circle and r.
Hence the value of tan 46° = y/x = 1.0355 (approx).
Tan 46° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 46 degrees as:
- sin(46°)/cos(46°)
- ± sin 46°/√(1 - sin²(46°))
- ± √(1 - cos²(46°))/cos 46°
- ± 1/√(cosec²(46°) - 1)
- ± √(sec²(46°) - 1)
- 1/cot 46°
Note: Since 46° lies in the 1st Quadrant, the final value of tan 46° will be positive.
We can use trigonometric identities to represent tan 46° as,
- cot(90° - 46°) = cot 44°
- -cot(90° + 46°) = -cot 136°
- -tan (180° - 46°) = -tan 134°
☛ Also Check:
FAQs on Tan 46 Degrees
What is Tan 46 Degrees?
Tan 46 degrees is the value of tangent trigonometric function for an angle equal to 46 degrees. The value of tan 46° is 1.0355 (approx).
What is the Value of Tan 46° in Terms of Sec 46°?
We can represent the tangent function in terms of the secant function using trig identities, tan 46° can be written as √(sec²(46°) - 1). Here, the value of sec 46° is equal to 1.4395.
What is the Value of Tan 46 Degrees in Terms of Cot 46°?
Since the tangent function is the reciprocal of the cotangent function, we can write tan 46° as 1/cot(46°). The value of cot 46° is equal to 0.96568.
How to Find Tan 46° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 46° can be given in terms of other trigonometric functions as:
- sin(46°)/cos(46°)
- ± sin 46°/√(1 - sin²(46°))
- ± √(1 - cos²(46°))/cos 46°
- ± 1/√(cosec²(46°) - 1)
- ± √(sec²(46°) - 1)
- 1/cot 46°
☛ Also check: trigonometric table
How to Find the Value of Tan 46 Degrees?
The value of tan 46 degrees can be calculated by constructing an angle of 46° with the x-axis, and then finding the coordinates of the corresponding point (0.6947, 0.7193) on the unit circle. The value of tan 46° is equal to the y-coordinate(0.7193) divided by the x-coordinate (0.6947). ∴ tan 46° = 1.0355