Tan 42 Degrees
The value of tan 42 degrees is 0.9004040. . .. Tan 42 degrees in radians is written as tan (42° × π/180°), i.e., tan (7π/30) or tan (0.733038. . .). In this article, we will discuss the methods to find the value of tan 42 degrees with examples.
- Tan 42° in decimal: 0.9004040. . .
- Tan (-42 degrees): -0.9004040. . .
- Tan 42° in radians: tan (7π/30) or tan (0.7330382 . . .)
What is the Value of Tan 42 Degrees?
The value of tan 42 degrees in decimal is 0.900404044. . .. Tan 42 degrees can also be expressed using the equivalent of the given angle (42 degrees) in radians (0.73303 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 42 degrees = 42° × (π/180°) rad = 7π/30 or 0.7330 . . .
∴ tan 42° = tan(0.7330) = 0.9004040. . .
Explanation:
For tan 42 degrees, the angle 42° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 42° value = 0.9004040. . .
Since the tangent function is a periodic function, we can represent tan 42° as, tan 42 degrees = tan(42° + n × 180°), n ∈ Z.
⇒ tan 42° = tan 222° = tan 402°, and so on.
Note: Since, tangent is an odd function, the value of tan(-42°) = -tan(42°).
Methods to Find Value of Tan 42 Degrees
The tangent function is positive in the 1st quadrant. The value of tan 42° is given as 0.90040. . .. We can find the value of tan 42 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Tan 42° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 42 degrees as:
- sin(42°)/cos(42°)
- ± sin 42°/√(1 - sin²(42°))
- ± √(1 - cos²(42°))/cos 42°
- ± 1/√(cosec²(42°) - 1)
- ± √(sec²(42°) - 1)
- 1/cot 42°
Note: Since 42° lies in the 1st Quadrant, the final value of tan 42° will be positive.
We can use trigonometric identities to represent tan 42° as,
- cot(90° - 42°) = cot 48°
- -cot(90° + 42°) = -cot 132°
- -tan (180° - 42°) = -tan 138°
Tan 42 Degrees Using Unit Circle
To find the value of tan 42 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 42° angle with the positive x-axis.
- The tan of 42 degrees equals the y-coordinate(0.6691) divided by x-coordinate(0.7431) of the point of intersection (0.7431, 0.6691) of unit circle and r.
Hence the value of tan 42° = y/x = 0.9004 (approx).
☛ Also Check:
FAQs on Tan 42 Degrees
What is Tan 42 Degrees?
Tan 42 degrees is the value of tangent trigonometric function for an angle equal to 42 degrees. The value of tan 42° is 0.9004 (approx).
What is the Exact Value of tan 42 Degrees?
The exact value of tan 42 degrees can be given accurately up to 8 decimal places as 0.90040404.
How to Find Tan 42° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 42° can be given in terms of other trigonometric functions as:
- sin(42°)/cos(42°)
- ± sin 42°/√(1 - sin²(42°))
- ± √(1 - cos²(42°))/cos 42°
- ± 1/√(cosec²(42°) - 1)
- ± √(sec²(42°) - 1)
- 1/cot 42°
☛ Also check: trigonometry table
What is the Value of Tan 42 Degrees in Terms of Cot 42°?
Since the tangent function is the reciprocal of the cotangent function, we can write tan 42° as 1/cot(42°). The value of cot 42° is equal to 1.11061.
How to Find the Value of Tan 42 Degrees?
The value of tan 42 degrees can be calculated by constructing an angle of 42° with the x-axis, and then finding the coordinates of the corresponding point (0.7431, 0.6691) on the unit circle. The value of tan 42° is equal to the y-coordinate(0.6691) divided by the x-coordinate (0.7431). ∴ tan 42° = 0.9004