Cos 34 Degrees
The value of cos 34 degrees is 0.8290375. . .. Cos 34 degrees in radians is written as cos (34° × π/180°), i.e., cos (17π/90) or cos (0.593411. . .). In this article, we will discuss the methods to find the value of cos 34 degrees with examples.
- Cos 34°: 0.8290375. . .
- Cos (-34 degrees): 0.8290375. . .
- Cos 34° in radians: cos (17π/90) or cos (0.5934119 . . .)
What is the Value of Cos 34 Degrees?
The value of cos 34 degrees in decimal is 0.829037572. . .. Cos 34 degrees can also be expressed using the equivalent of the given angle (34 degrees) in radians (0.59341 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 34 degrees = 34° × (π/180°) rad = 17π/90 or 0.5934 . . .
∴ cos 34° = cos(0.5934) = 0.8290375. . .
Explanation:
For cos 34 degrees, the angle 34° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 34° value = 0.8290375. . .
Since the cosine function is a periodic function, we can represent cos 34° as, cos 34 degrees = cos(34° + n × 360°), n ∈ Z.
⇒ cos 34° = cos 394° = cos 754°, and so on.
Note: Since, cosine is an even function, the value of cos(-34°) = cos(34°).
Methods to Find Value of Cos 34 Degrees
The cosine function is positive in the 1st quadrant. The value of cos 34° is given as 0.82903. . .. We can find the value of cos 34 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Cos 34° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 34 degrees as:
- ± √(1-sin²(34°))
- ± 1/√(1 + tan²(34°))
- ± cot 34°/√(1 + cot²(34°))
- ±√(cosec²(34°) - 1)/cosec 34°
- 1/sec 34°
Note: Since 34° lies in the 1st Quadrant, the final value of cos 34° will be positive.
We can use trigonometric identities to represent cos 34° as,
- -cos(180° - 34°) = -cos 146°
- -cos(180° + 34°) = -cos 214°
- sin(90° + 34°) = sin 124°
- sin(90° - 34°) = sin 56°
Cos 34 Degrees Using Unit Circle
To find the value of cos 34 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 34° angle with the positive x-axis.
- The cos of 34 degrees equals the x-coordinate(0.829) of the point of intersection (0.829, 0.5592) of unit circle and r.
Hence the value of cos 34° = x = 0.829 (approx)
☛ Also Check:
FAQs on Cos 34 Degrees
What is Cos 34 Degrees?
Cos 34 degrees is the value of cosine trigonometric function for an angle equal to 34 degrees. The value of cos 34° is 0.829 (approx)
How to Find Cos 34° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 34° can be given in terms of other trigonometric functions as:
- ± √(1-sin²(34°))
- ± 1/√(1 + tan²(34°))
- ± cot 34°/√(1 + cot²(34°))
- ± √(cosec²(34°) - 1)/cosec 34°
- 1/sec 34°
☛ Also check: trigonometry table
What is the Value of Cos 34° in Terms of Cosec 34°?
Since the cosine function can be represented using the cosecant function, we can write cos 34° as [√(cosec²(34°) - 1)/cosec 34°]. The value of cosec 34° is equal to 1.78829.
What is the Value of Cos 34 Degrees in Terms of Cot 34°?
We can represent the cosine function in terms of the cotangent function using trig identities, cos 34° can be written as cot 34°/√(1 + cot²(34°)). Here, the value of cot 34° is equal to 1.48256.
How to Find the Value of Cos 34 Degrees?
The value of cos 34 degrees can be calculated by constructing an angle of 34° with the x-axis, and then finding the coordinates of the corresponding point (0.829, 0.5592) on the unit circle. The value of cos 34° is equal to the x-coordinate (0.829). ∴ cos 34° = 0.829.