Tan 52 Degrees
The value of tan 52 degrees is 1.2799416. . .. Tan 52 degrees in radians is written as tan (52° × π/180°), i.e., tan (13π/45) or tan (0.907571. . .). In this article, we will discuss the methods to find the value of tan 52 degrees with examples.
- Tan 52° in decimal: 1.2799416. . .
- Tan (-52 degrees): -1.2799416. . .
- Tan 52° in radians: tan (13π/45) or tan (0.9075712 . . .)
What is the Value of Tan 52 Degrees?
The value of tan 52 degrees in decimal is 1.279941632. . .. Tan 52 degrees can also be expressed using the equivalent of the given angle (52 degrees) in radians (0.90757 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 52 degrees = 52° × (π/180°) rad = 13π/45 or 0.9075 . . .
∴ tan 52° = tan(0.9075) = 1.2799416. . .
Explanation:
For tan 52 degrees, the angle 52° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 52° value = 1.2799416. . .
Since the tangent function is a periodic function, we can represent tan 52° as, tan 52 degrees = tan(52° + n × 180°), n ∈ Z.
⇒ tan 52° = tan 232° = tan 412°, and so on.
Note: Since, tangent is an odd function, the value of tan(-52°) = -tan(52°).
Methods to Find Value of Tan 52 Degrees
The tangent function is positive in the 1st quadrant. The value of tan 52° is given as 1.27994. . .. We can find the value of tan 52 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Tan 52 Degrees Using Unit Circle
To find the value of tan 52 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 52° angle with the positive x-axis.
- The tan of 52 degrees equals the y-coordinate(0.788) divided by x-coordinate(0.6157) of the point of intersection (0.6157, 0.788) of unit circle and r.
Hence the value of tan 52° = y/x = 1.2799 (approx).
Tan 52° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 52 degrees as:
- sin(52°)/cos(52°)
- ± sin 52°/√(1 - sin²(52°))
- ± √(1 - cos²(52°))/cos 52°
- ± 1/√(cosec²(52°) - 1)
- ± √(sec²(52°) - 1)
- 1/cot 52°
Note: Since 52° lies in the 1st Quadrant, the final value of tan 52° will be positive.
We can use trigonometric identities to represent tan 52° as,
- cot(90° - 52°) = cot 38°
- -cot(90° + 52°) = -cot 142°
- -tan (180° - 52°) = -tan 128°
☛ Also Check:
FAQs on Tan 52 Degrees
What is Tan 52 Degrees?
Tan 52 degrees is the value of tangent trigonometric function for an angle equal to 52 degrees. The value of tan 52° is 1.2799 (approx).
How to Find Tan 52° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 52° can be given in terms of other trigonometric functions as:
- sin(52°)/cos(52°)
- ± sin 52°/√(1 - sin²(52°))
- ± √(1 - cos²(52°))/cos 52°
- ± 1/√(cosec²(52°) - 1)
- ± √(sec²(52°) - 1)
- 1/cot 52°
☛ Also check: trigonometry table
What is the Value of Tan 52 Degrees in Terms of Sin 52°?
Using trigonometric identities, we can write tan 52° in terms of sin 52° as, tan(52°) = sin 52°/√(1 - sin²(52°)) . Here, the value of sin 52° is equal to 0.788.
What is the Value of Tan 52° in Terms of Sec 52°?
We can represent the tangent function in terms of the secant function using trig identities, tan 52° can be written as √(sec²(52°) - 1). Here, the value of sec 52° is equal to 1.6242.
How to Find the Value of Tan 52 Degrees?
The value of tan 52 degrees can be calculated by constructing an angle of 52° with the x-axis, and then finding the coordinates of the corresponding point (0.6157, 0.788) on the unit circle. The value of tan 52° is equal to the y-coordinate(0.788) divided by the x-coordinate (0.6157). ∴ tan 52° = 1.2799