Tan 195 Degrees
The value of tan 195 degrees is 0.2679491. . .. Tan 195 degrees in radians is written as tan (195° × π/180°), i.e., tan (13π/12) or tan (3.403392. . .). In this article, we will discuss the methods to find the value of tan 195 degrees with examples.
- Tan 195°: 2 - √3
- Tan 195° in decimal: 0.2679491. . .
- Tan (-195 degrees): -0.2679491. . . or -2 + √3
- Tan 195° in radians: tan (13π/12) or tan (3.4033920 . . .)
What is the Value of Tan 195 Degrees?
The value of tan 195 degrees in decimal is 0.267949192. . .. Tan 195 degrees can also be expressed using the equivalent of the given angle (195 degrees) in radians (3.40339 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 195 degrees = 195° × (π/180°) rad = 13π/12 or 3.4033 . . .
∴ tan 195° = tan(3.4033) = 2 - √3 or 0.2679491. . .
Explanation:
For tan 195 degrees, the angle 195° lies between 180° and 270° (Third Quadrant). Since tangent function is positive in the third quadrant, thus tan 195° value = 2 - √3 or 0.2679491. . .
Since the tangent function is a periodic function, we can represent tan 195° as, tan 195 degrees = tan(195° + n × 180°), n ∈ Z.
⇒ tan 195° = tan 375° = tan 555°, and so on.
Note: Since, tangent is an odd function, the value of tan(-195°) = -tan(195°).
Methods to Find Value of Tan 195 Degrees
The tangent function is positive in the 3rd quadrant. The value of tan 195° is given as 0.26794. . .. We can find the value of tan 195 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Tan 195° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 195 degrees as:
- sin(195°)/cos(195°)
- ± sin 195°/√(1 - sin²(195°))
- ± √(1 - cos²(195°))/cos 195°
- ± 1/√(cosec²(195°) - 1)
- ± √(sec²(195°) - 1)
- 1/cot 195°
Note: Since 195° lies in the 3rd Quadrant, the final value of tan 195° will be positive.
We can use trigonometric identities to represent tan 195° as,
- cot(90° - 195°) = cot(-105°)
- -cot(90° + 195°) = -cot 285°
- -tan (180° - 195°) = -tan(-15°)
Tan 195 Degrees Using Unit Circle
To find the value of tan 195 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 195° angle with the positive x-axis.
- The tan of 195 degrees equals the y-coordinate(-0.2588) divided by x-coordinate(-0.9659) of the point of intersection (-0.9659, -0.2588) of unit circle and r.
Hence the value of tan 195° = y/x = 0.2679 (approx).
☛ Also Check:
FAQs on Tan 195 Degrees
What is Tan 195 Degrees?
Tan 195 degrees is the value of tangent trigonometric function for an angle equal to 195 degrees. The value of tan 195° is 2 - √3 or 0.2679 (approx).
What is the Value of Tan 195 Degrees in Terms of Cos 195°?
We know, using trig identities, we can write tan 195° as -√(1 - cos²(195°))/cos 195°. Here, the value of cos 195° is equal to -0.965925.
What is the Value of Tan 195° in Terms of Cosec 195°?
Since the tangent function can be represented using the cosecant function, we can write tan 195° as 1/√(cosec²(195°) - 1). The value of cosec 195° is equal to -3.86370.
How to Find Tan 195° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 195° can be given in terms of other trigonometric functions as:
- sin(195°)/cos(195°)
- ± sin 195°/√(1 - sin²(195°))
- ± √(1 - cos²(195°))/cos 195°
- ± 1/√(cosec²(195°) - 1)
- ± √(sec²(195°) - 1)
- 1/cot 195°
☛ Also check: trigonometry table
How to Find the Value of Tan 195 Degrees?
The value of tan 195 degrees can be calculated by constructing an angle of 195° with the x-axis, and then finding the coordinates of the corresponding point (-0.9659, -0.2588) on the unit circle. The value of tan 195° is equal to the y-coordinate(-0.2588) divided by the x-coordinate (-0.9659). ∴ tan 195° = 2 - √3 or 0.2679