Cot 70 Degrees
The value of cot 70 degrees is 0.3639702. . .. Cot 70 degrees in radians is written as cot (70° × π/180°), i.e., cot (7π/18) or cot (1.221730. . .). In this article, we will discuss the methods to find the value of cot 70 degrees with examples.
- Cot 70° in decimal: 0.3639702. . .
- Cot (-70 degrees): -0.3639702. . .
- Cot 70° in radians: cot (7π/18) or cot (1.2217304 . . .)
What is the Value of Cot 70 Degrees?
The value of cot 70 degrees in decimal is 0.363970234. . .. Cot 70 degrees can also be expressed using the equivalent of the given angle (70 degrees) in radians (1.22173 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 70 degrees = 70° × (π/180°) rad = 7π/18 or 1.2217 . . .
∴ cot 70° = cot(1.2217) = 0.3639702. . .
Explanation:
For cot 70 degrees, the angle 70° lies between 0° and 90° (First Quadrant). Since cotangent function is positive in the first quadrant, thus cot 70° value = 0.3639702. . .
Since the cotangent function is a periodic function, we can represent cot 70° as, cot 70 degrees = cot(70° + n × 180°), n ∈ Z.
⇒ cot 70° = cot 250° = cot 430°, and so on.
Note: Since, cotangent is an odd function, the value of cot(-70°) = -cot(70°).
Methods to Find Value of Cot 70 Degrees
The cotangent function is positive in the 1st quadrant. The value of cot 70° is given as 0.36397. . . We can find the value of cot 70 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Cot 70 Degrees Using Unit Circle
To find the value of cot 70 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 70° angle with the positive x-axis.
- The cot of 70 degrees equals the x-coordinate(0.342) divided by y-coordinate(0.9397) of the point of intersection (0.342, 0.9397) of unit circle and r.
Hence the value of cot 70° = x/y = 0.364 (approx).
Cot 70° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 70 degrees as:
- cos(70°)/sin(70°)
- ± cos 70°/√(1 - cos²(70°))
- ± √(1 - sin²(70°))/sin 70°
- ± 1/√(sec²(70°) - 1)
- ± √(cosec²(70°) - 1)
- 1/tan 70°
Note: Since 70° lies in the 1st Quadrant, the final value of cot 70° will be positive.
We can use trigonometric identities to represent cot 70° as,
- tan (90° - 70°) = tan 20°
- -tan (90° + 70°) = -tan 160°
- -cot (180° - 70°) = -cot 110°
☛ Also Check:
FAQs on Cot 70 Degrees
What is Cot 70 Degrees?
Cot 70 degrees is the value of cotangent trigonometric function for an angle equal to 70 degrees. The value of cot 70° is 0.364 (approx).
What is the Value of Cot 70 Degrees in Terms of Tan 70°?
Since the cotangent function is the reciprocal of the tangent function, we can write cot 70° as 1/tan(70°). The value of tan 70° is equal to 2.74747.
How to Find Cot 70° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 70° can be given in terms of other trigonometric functions as:
- cos(70°)/sin(70°)
- ± cos 70°/√(1 - cos²(70°))
- ± √(1 - sin²(70°))/sin 70°
- ± 1/√(sec²(70°) - 1)
- ± √(cosec²(70°) - 1)
- 1/tan 70°
☛ Also check: trigonometry table
How to Find the Value of Cot 70 Degrees?
The value of cot 70 degrees can be calculated by constructing an angle of 70° with the x-axis, and then finding the coordinates of the corresponding point (0.342, 0.9397) on the unit circle. The value of cot 70° is equal to the x-coordinate(0.342) divided by the y-coordinate (0.9397). ∴ cot 70° = 0.364
What is the Value of Cot 70° in Terms of Sec 70°?
We can represent the cotangent function in terms of the secant function using trig identities, cot 70° can be written as 1/√(sec²(70°) - 1). Here, the value of sec 70° is equal to 2.9238.