Cos 144 Degrees
The value of cos 144 degrees is -0.8090169. . .. Cos 144 degrees in radians is written as cos (144° × π/180°), i.e., cos (4π/5) or cos (2.513274. . .). In this article, we will discuss the methods to find the value of cos 144 degrees with examples.
- Cos 144°: -0.8090169. . .
- Cos 144° in fraction: (-1 - √5)/4
- Cos (-144 degrees): -0.8090169. . .
- Cos 144° in radians: cos (4π/5) or cos (2.5132741 . . .)
What is the Value of Cos 144 Degrees?
The value of cos 144 degrees in decimal is -0.809016994. . .. Cos 144 degrees can also be expressed using the equivalent of the given angle (144 degrees) in radians (2.51327 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 144 degrees = 144° × (π/180°) rad = 4π/5 or 2.5132 . . .
∴ cos 144° = cos(2.5132) = (-1 - √5)/4 or -0.8090169. . .
Explanation:
For cos 144 degrees, the angle 144° lies between 90° and 180° (Second Quadrant). Since cosine function is negative in the second quadrant, thus cos 144° value = (-1 - √5)/4 or -0.8090169. . .
Since the cosine function is a periodic function, we can represent cos 144° as, cos 144 degrees = cos(144° + n × 360°), n ∈ Z.
⇒ cos 144° = cos 504° = cos 864°, and so on.
Note: Since, cosine is an even function, the value of cos(-144°) = cos(144°).
Methods to Find Value of Cos 144 Degrees
The cosine function is negative in the 2nd quadrant. The value of cos 144° is given as -0.80901. . .. We can find the value of cos 144 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Cos 144° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 144 degrees as:
- ± √(1-sin²(144°))
- ± 1/√(1 + tan²(144°))
- ± cot 144°/√(1 + cot²(144°))
- ±√(cosec²(144°) - 1)/cosec 144°
- 1/sec 144°
Note: Since 144° lies in the 2nd Quadrant, the final value of cos 144° will be negative.
We can use trigonometric identities to represent cos 144° as,
- -cos(180° - 144°) = -cos 36°
- -cos(180° + 144°) = -cos 324°
- sin(90° + 144°) = sin 234°
- sin(90° - 144°) = sin(-54°)
Cos 144 Degrees Using Unit Circle
To find the value of cos 144 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 144° angle with the positive x-axis.
- The cos of 144 degrees equals the x-coordinate(-0.809) of the point of intersection (-0.809, 0.5878) of unit circle and r.
Hence the value of cos 144° = x = -0.809 (approx)
☛ Also Check:
FAQs on Cos 144 Degrees
What is Cos 144 Degrees?
Cos 144 degrees is the value of cosine trigonometric function for an angle equal to 144 degrees. The value of cos 144° is (-1 - √5)/4 or -0.809 (approx)
How to Find Cos 144° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 144° can be given in terms of other trigonometric functions as:
- ± √(1-sin²(144°))
- ± 1/√(1 + tan²(144°))
- ± cot 144°/√(1 + cot²(144°))
- ± √(cosec²(144°) - 1)/cosec 144°
- 1/sec 144°
☛ Also check: trigonometric table
How to Find the Value of Cos 144 Degrees?
The value of cos 144 degrees can be calculated by constructing an angle of 144° with the x-axis, and then finding the coordinates of the corresponding point (-0.809, 0.5878) on the unit circle. The value of cos 144° is equal to the x-coordinate (-0.809). ∴ cos 144° = -0.809.
What is the Value of Cos 144 Degrees in Terms of Tan 144°?
We know, using trig identities, we can write cos 144° as -1/√(1 + tan²(144°)). Here, the value of tan 144° is equal to -0.726542.
What is the Value of Cos 144° in Terms of Cosec 144°?
Since the cosine function can be represented using the cosecant function, we can write cos 144° as -[√(cosec²(144°) - 1)/cosec 144°]. The value of cosec 144° is equal to 1.70130.