The value of tan 30 degrees is equal to 0.577. Converting degree to radians, that is, θ (radians) = θ × π/180 °. The value of tan 30 degrees is calculated by various methods, including the formula of the trigonometric ratio.
- Tan 30° = 1/√3 = √3/3
- Tan 30° in decimal = 0.577
- Tan 30° in radians =Tan (π/6) or Tan (0.5235) = 0.577
- Tan (-30°) = -0.577
Tan 30 Degree Derivation
We can derive the value of tan 30 Degree using the graphical method.
Consider an equilateral triangle PQR where,
PQ = QR = RP and ∠P = ∠Q = ∠R = 60°. …………….(1)
Draw a perpendicular bisector PS of the line QR from vertex P.
Now, QS = RS, and PS = √3 (when QS = 1 and PQ = 2)
In a right-angle triangle PQS
tan 30° = Perpendicular / Base
Here,
Perpendicular = QS
Base = PS
tan 30° = QS / PS
tan 30° = 1/√3
Thus, the value of tan 30° is 1/√3
Also Read:
Tan 30 Degrees in Terms of Trigonometric Functions
Trigonometric functions are also called circular functions or trigonometric ratios. The relationship between angles and sides is represented by these trigonometric functions. The representation of the value of tan 30° using trigonometric functions is:
- Tan 30° = ± √(sec2 30° - 1)
- Tan 30° = 1/cot 30°
