Cos 68 Degrees
The value of cos 68 degrees is 0.3746065. . .. Cos 68 degrees in radians is written as cos (68° × π/180°), i.e., cos (17π/45) or cos (1.186823. . .). In this article, we will discuss the methods to find the value of cos 68 degrees with examples.
- Cos 68°: 0.3746065. . .
- Cos (-68 degrees): 0.3746065. . .
- Cos 68° in radians: cos (17π/45) or cos (1.1868238 . . .)
What is the Value of Cos 68 Degrees?
The value of cos 68 degrees in decimal is 0.374606593. . .. Cos 68 degrees can also be expressed using the equivalent of the given angle (68 degrees) in radians (1.18682 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 68 degrees = 68° × (π/180°) rad = 17π/45 or 1.1868 . . .
∴ cos 68° = cos(1.1868) = 0.3746065. . .
Explanation:
For cos 68 degrees, the angle 68° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 68° value = 0.3746065. . .
Since the cosine function is a periodic function, we can represent cos 68° as, cos 68 degrees = cos(68° + n × 360°), n ∈ Z.
⇒ cos 68° = cos 428° = cos 788°, and so on.
Note: Since, cosine is an even function, the value of cos(-68°) = cos(68°).
Methods to Find Value of Cos 68 Degrees
The cosine function is positive in the 1st quadrant. The value of cos 68° is given as 0.37460. . .. We can find the value of cos 68 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Cos 68° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 68 degrees as:
- ± √(1-sin²(68°))
- ± 1/√(1 + tan²(68°))
- ± cot 68°/√(1 + cot²(68°))
- ±√(cosec²(68°) - 1)/cosec 68°
- 1/sec 68°
Note: Since 68° lies in the 1st Quadrant, the final value of cos 68° will be positive.
We can use trigonometric identities to represent cos 68° as,
- -cos(180° - 68°) = -cos 112°
- -cos(180° + 68°) = -cos 248°
- sin(90° + 68°) = sin 158°
- sin(90° - 68°) = sin 22°
Cos 68 Degrees Using Unit Circle
To find the value of cos 68 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 68° angle with the positive x-axis.
- The cos of 68 degrees equals the x-coordinate(0.3746) of the point of intersection (0.3746, 0.9272) of unit circle and r.
Hence the value of cos 68° = x = 0.3746 (approx)
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FAQs on Cos 68 Degrees
What is Cos 68 Degrees?
Cos 68 degrees is the value of cosine trigonometric function for an angle equal to 68 degrees. The value of cos 68° is 0.3746 (approx)
How to Find the Value of Cos 68 Degrees?
The value of cos 68 degrees can be calculated by constructing an angle of 68° with the x-axis, and then finding the coordinates of the corresponding point (0.3746, 0.9272) on the unit circle. The value of cos 68° is equal to the x-coordinate (0.3746). ∴ cos 68° = 0.3746.
What is the Value of Cos 68° in Terms of Sec 68°?
Since the secant function is the reciprocal of the cosine function, we can write cos 68° as 1/sec(68°). The value of sec 68° is equal to 2.669467.
What is the Value of Cos 68 Degrees in Terms of Tan 68°?
We know, using trig identities, we can write cos 68° as 1/√(1 + tan²(68°)). Here, the value of tan 68° is equal to 2.475086.
How to Find Cos 68° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 68° can be given in terms of other trigonometric functions as:
- ± √(1-sin²(68°))
- ± 1/√(1 + tan²(68°))
- ± cot 68°/√(1 + cot²(68°))
- ± √(cosec²(68°) - 1)/cosec 68°
- 1/sec 68°
☛ Also check: trigonometry table