Tan 1050 Degrees
The value of tan 1050 degrees is -0.5773502. . .. Tan 1050 degrees in radians is written as tan (1050° × π/180°), i.e., tan (35π/6) or tan (18.325957. . .). In this article, we will discuss the methods to find the value of tan 1050 degrees with examples.
- Tan 1050°: -1/√3
- Tan 1050° in decimal: -0.5773502. . .
- Tan (-1050 degrees): 0.5773502. . . or 1/√3
- Tan 1050° in radians: tan (35π/6) or tan (18.3259571 . . .)
What is the Value of Tan 1050 Degrees?
The value of tan 1050 degrees in decimal is -0.577350269. . .. Tan 1050 degrees can also be expressed using the equivalent of the given angle (1050 degrees) in radians (18.32595 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 1050 degrees = 1050° × (π/180°) rad = 35π/6 or 18.3259 . . .
∴ tan 1050° = tan(18.3259) = -1/√3 or -0.5773502. . .
Explanation:
For tan 1050°, the angle 1050° > 360°. We can represent tan 1050° as, tan(1050° mod 360°) = tan(330°). The angle 1050°, coterminal to angle 330°, is located in the Fourth Quadrant(Quadrant IV).
Since tangent function is negative in the 4th quadrant, thus tan 1050 degrees value = -1/√3 or -0.5773502. . .
Similarly, given the periodic property of tan 1050°, it can also be written as, tan 1050 degrees = (1050° + n × 180°), n ∈ Z.
⇒ tan 1050° = tan 1230° = tan 1410°, and so on.
Note: Since, tangent is an odd function, the value of tan(-1050°) = -tan(1050°).
Methods to Find Value of Tan 1050 Degrees
The tangent function is negative in the 4th quadrant. The value of tan 1050° is given as -0.57735. . .. We can find the value of tan 1050 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Tan 1050° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 1050 degrees as:
- sin(1050°)/cos(1050°)
- ± sin 1050°/√(1 - sin²(1050°))
- ± √(1 - cos²(1050°))/cos 1050°
- ± 1/√(cosec²(1050°) - 1)
- ± √(sec²(1050°) - 1)
- 1/cot 1050°
Note: Since 1050° lies in the 4th Quadrant, the final value of tan 1050° will be negative.
We can use trigonometric identities to represent tan 1050° as,
- cot(90° - 1050°) = cot(-960°)
- -cot(90° + 1050°) = -cot 1140°
- -tan (180° - 1050°) = -tan(-870°)
Tan 1050 Degrees Using Unit Circle
To find the value of tan 1050 degrees using the unit circle, represent 1050° in the form (2 × 360°) + 330° [∵ 1050°>360°] ∵ The angle 1050° is coterminal to 330° angle and also tangent is a periodic function, tan 1050° = tan 330°.
- Rotate ‘r’ anticlockwise to form 330° or 1050° angle with the positive x-axis.
- The tan of 1050 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 1050° = y/x = -0.5774 (approx).
☛ Also Check:
FAQs on Tan 1050 Degrees
What is Tan 1050 Degrees?
Tan 1050 degrees is the value of tangent trigonometric function for an angle equal to 1050 degrees. The value of tan 1050° is -1/√3 or -0.5774 (approx).
How to Find Tan 1050° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 1050° can be given in terms of other trigonometric functions as:
- sin(1050°)/cos(1050°)
- ± sin 1050°/√(1 - sin²(1050°))
- ± √(1 - cos²(1050°))/cos 1050°
- ± 1/√(cosec²(1050°) - 1)
- ± √(sec²(1050°) - 1)
- 1/cot 1050°
☛ Also check: trigonometry table
How to Find the Value of Tan 1050 Degrees?
The value of tan 1050 degrees can be calculated by constructing an angle of 1050° 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 1050° is equal to the y-coordinate(-0.5) divided by the x-coordinate (0.866). ∴ tan 1050° = -1/√3 or -0.5774
What is the Exact Value of tan 1050 Degrees?
The exact value of tan 1050 degrees can be given accurately up to 8 decimal places as -0.57735026 or as -1/√3.
What is the Value of Tan 1050 Degrees in Terms of Sin 1050°?
Using trigonometric identities, we can write tan 1050° in terms of sin 1050° as, tan(1050°) = sin 1050°/√(1 - sin²(1050°)) . Here, the value of sin 1050° is equal to -0.5.