Tan 1125 Degrees
The value of tan 1125 degrees is 1. Tan 1125 degrees in radians is written as tan (1125° × π/180°), i.e., tan (25π/4) or tan (19.634954. . .). In this article, we will discuss the methods to find the value of tan 1125 degrees with examples.
- Tan 1125°: 1
- Tan (-1125 degrees): -1
- Tan 1125° in radians: tan (25π/4) or tan (19.6349540 . . .)
What is the Value of Tan 1125 Degrees?
The value of tan 1125 degrees is 1. Tan 1125 degrees can also be expressed using the equivalent of the given angle (1125 degrees) in radians (19.63495 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 1125 degrees = 1125° × (π/180°) rad = 25π/4 or 19.6349 . . .
∴ tan 1125° = tan(19.6349) = 1
Explanation:
For tan 1125°, the angle 1125° > 360°. We can represent tan 1125° as, tan(1125° mod 360°) = tan(45°). The angle 1125°, coterminal to angle 45°, is located in the First Quadrant(Quadrant I).
Since tangent function is positive in the 1st quadrant, thus tan 1125 degrees value = 1
Similarly, given the periodic property of tan 1125°, it can also be written as, tan 1125 degrees = (1125° + n × 180°), n ∈ Z.
⇒ tan 1125° = tan 1305° = tan 1485°, and so on.
Note: Since, tangent is an odd function, the value of tan(-1125°) = -tan(1125°).
Methods to Find Value of Tan 1125 Degrees
The tangent function is positive in the 1st quadrant. The value of tan 1125° is given as 1. We can find the value of tan 1125 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Tan 1125° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 1125 degrees as:
- sin(1125°)/cos(1125°)
- ± sin 1125°/√(1 - sin²(1125°))
- ± √(1 - cos²(1125°))/cos 1125°
- ± 1/√(cosec²(1125°) - 1)
- ± √(sec²(1125°) - 1)
- 1/cot 1125°
Note: Since 1125° lies in the 1st Quadrant, the final value of tan 1125° will be positive.
We can use trigonometric identities to represent tan 1125° as,
- cot(90° - 1125°) = cot(-1035°)
- -cot(90° + 1125°) = -cot 1215°
- -tan (180° - 1125°) = -tan(-945°)
Tan 1125 Degrees Using Unit Circle
To find the value of tan 1125 degrees using the unit circle, represent 1125° in the form (3 × 360°) + 45° [∵ 1125°>360°] ∵ The angle 1125° is coterminal to 45° angle and also tangent is a periodic function, tan 1125° = tan 45°.
- Rotate ‘r’ anticlockwise to form 45° or 1125° angle with the positive x-axis.
- The tan of 1125 degrees equals the y-coordinate(0.7071) divided by x-coordinate(0.7071) of the point of intersection (0.7071, 0.7071) of unit circle and r.
Hence the value of tan 1125° = y/x = 1
☛ Also Check:
FAQs on Tan 1125 Degrees
What is Tan 1125 Degrees?
Tan 1125 degrees is the value of tangent trigonometric function for an angle equal to 1125 degrees. The value of tan 1125° is 1.
How to Find the Value of Tan 1125 Degrees?
The value of tan 1125 degrees can be calculated by constructing an angle of 1125° with the x-axis, and then finding the coordinates of the corresponding point (0.7071, 0.7071) on the unit circle. The value of tan 1125° is equal to the y-coordinate(0.7071) divided by the x-coordinate (0.7071). ∴ tan 1125° = 1
How to Find Tan 1125° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 1125° can be given in terms of other trigonometric functions as:
- sin(1125°)/cos(1125°)
- ± sin 1125°/√(1 - sin²(1125°))
- ± √(1 - cos²(1125°))/cos 1125°
- ± 1/√(cosec²(1125°) - 1)
- ± √(sec²(1125°) - 1)
- 1/cot 1125°
☛ Also check: trigonometry table
What is the Value of Tan 1125 Degrees in Terms of Cos 1125°?
We know, using trig identities, we can write tan 1125° as √(1 - cos²(1125°))/cos 1125°. Here, the value of cos 1125° is equal to 0.707106.
What is the Value of Tan 1125° in Terms of Sec 1125°?
We can represent the tangent function in terms of the secant function using trig identities, tan 1125° can be written as √(sec²(1125°) - 1). Here, the value of sec 1125° is equal to 1.4142.