Tan 150 Degrees
The value of tan 150 degrees is -0.5773502. . .. Tan 150 degrees in radians is written as tan (150° × π/180°), i.e., tan (5π/6) or tan (2.617993. . .). In this article, we will discuss the methods to find the value of tan 150 degrees with examples.
- Tan 150°: -1/√3
- Tan 150° in decimal: -0.5773502. . .
- Tan (-150 degrees): 0.5773502. . . or 1/√3
- Tan 150° in radians: tan (5π/6) or tan (2.6179938 . . .)
What is the Value of Tan 150 Degrees?
The value of tan 150 degrees in decimal is -0.577350269. . .. Tan 150 degrees can also be expressed using the equivalent of the given angle (150 degrees) in radians (2.61799 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 150 degrees = 150° × (π/180°) rad = 5π/6 or 2.6179 . . .
∴ tan 150° = tan(2.6179) = -1/√3 or -0.5773502. . .
Explanation:
For tan 150 degrees, the angle 150° lies between 90° and 180° (Second Quadrant). Since tangent function is negative in the second quadrant, thus tan 150° value = -1/√3 or -0.5773502. . .
Since the tangent function is a periodic function, we can represent tan 150° as, tan 150 degrees = tan(150° + n × 180°), n ∈ Z.
⇒ tan 150° = tan 330° = tan 510°, and so on.
Note: Since, tangent is an odd function, the value of tan(-150°) = -tan(150°).
Methods to Find Value of Tan 150 Degrees
The tangent function is negative in the 2nd quadrant. The value of tan 150° is given as -0.57735. . .. We can find the value of tan 150 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Tan 150° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 150 degrees as:
- sin(150°)/cos(150°)
- ± sin 150°/√(1 - sin²(150°))
- ± √(1 - cos²(150°))/cos 150°
- ± 1/√(cosec²(150°) - 1)
- ± √(sec²(150°) - 1)
- 1/cot 150°
Note: Since 150° lies in the 2nd Quadrant, the final value of tan 150° will be negative.
We can use trigonometric identities to represent tan 150° as,
- cot(90° - 150°) = cot(-60°)
- -cot(90° + 150°) = -cot 240°
- -tan (180° - 150°) = -tan 30°
Tan 150 Degrees Using Unit Circle
To find the value of tan 150 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 150° angle with the positive x-axis.
- The tan of 150 degrees equals the y-coordinate(0.5) divided by x-coordinate(-0.866) of the point of intersection (-0.866, 0.5) of unit circle and r.
Hence the value of tan 150° = y/x = -0.5774 (approx).
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FAQs on Tan 150 Degrees
What is Tan 150 Degrees?
Tan 150 degrees is the value of tangent trigonometric function for an angle equal to 150 degrees. The value of tan 150° is -1/√3 or -0.5774 (approx).
What is the Value of Tan 150 Degrees in Terms of Cot 150°?
Since the tangent function is the reciprocal of the cotangent function, we can write tan 150° as 1/cot(150°). The value of cot 150° is equal to -√3.
What is the Value of Tan 150° in Terms of Cosec 150°?
Since the tangent function can be represented using the cosecant function, we can write tan 150° as -1/√(cosec²(150°) - 1). The value of cosec 150° is equal to 2.
How to Find the Value of Tan 150 Degrees?
The value of tan 150 degrees can be calculated by constructing an angle of 150° with the x-axis, and then finding the coordinates of the corresponding point (-0.866, 0.5) on the unit circle. The value of tan 150° is equal to the y-coordinate(0.5) divided by the x-coordinate (-0.866). ∴ tan 150° = -1/√3 or -0.5774
How to Find Tan 150° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 150° can be given in terms of other trigonometric functions as:
- sin(150°)/cos(150°)
- ± sin 150°/√(1 - sin²(150°))
- ± √(1 - cos²(150°))/cos 150°
- ± 1/√(cosec²(150°) - 1)
- ± √(sec²(150°) - 1)
- 1/cot 150°
☛ Also check: trigonometry table