Cos 49 Degrees
The value of cos 49 degrees is 0.6560590. . .. Cos 49 degrees in radians is written as cos (49° × π/180°), i.e., cos (0.855211. . .). In this article, we will discuss the methods to find the value of cos 49 degrees with examples.
- Cos 49°: 0.6560590. . .
- Cos (-49 degrees): 0.6560590. . .
- Cos 49° in radians: cos (0.8552113 . . .)
What is the Value of Cos 49 Degrees?
The value of cos 49 degrees in decimal is 0.656059028. . .. Cos 49 degrees can also be expressed using the equivalent of the given angle (49 degrees) in radians (0.85521 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 49 degrees = 49° × (π/180°) rad = 0.8552 . . .
∴ cos 49° = cos(0.8552) = 0.6560590. . .
Explanation:
For cos 49 degrees, the angle 49° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 49° value = 0.6560590. . .
Since the cosine function is a periodic function, we can represent cos 49° as, cos 49 degrees = cos(49° + n × 360°), n ∈ Z.
⇒ cos 49° = cos 409° = cos 769°, and so on.
Note: Since, cosine is an even function, the value of cos(-49°) = cos(49°).
Methods to Find Value of Cos 49 Degrees
The cosine function is positive in the 1st quadrant. The value of cos 49° is given as 0.65605. . .. We can find the value of cos 49 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Cos 49 Degrees Using Unit Circle
To find the value of cos 49 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 49° angle with the positive x-axis.
- The cos of 49 degrees equals the x-coordinate(0.6561) of the point of intersection (0.6561, 0.7547) of unit circle and r.
Hence the value of cos 49° = x = 0.6561 (approx)
Cos 49° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 49 degrees as:
- ± √(1-sin²(49°))
- ± 1/√(1 + tan²(49°))
- ± cot 49°/√(1 + cot²(49°))
- ±√(cosec²(49°) - 1)/cosec 49°
- 1/sec 49°
Note: Since 49° lies in the 1st Quadrant, the final value of cos 49° will be positive.
We can use trigonometric identities to represent cos 49° as,
- -cos(180° - 49°) = -cos 131°
- -cos(180° + 49°) = -cos 229°
- sin(90° + 49°) = sin 139°
- sin(90° - 49°) = sin 41°
☛ Also Check:
FAQs on Cos 49 Degrees
What is Cos 49 Degrees?
Cos 49 degrees is the value of cosine trigonometric function for an angle equal to 49 degrees. The value of cos 49° is 0.6561 (approx)
What is the Value of Cos 49° in Terms of Sec 49°?
Since the secant function is the reciprocal of the cosine function, we can write cos 49° as 1/sec(49°). The value of sec 49° is equal to 1.524253.
How to Find the Value of Cos 49 Degrees?
The value of cos 49 degrees can be calculated by constructing an angle of 49° with the x-axis, and then finding the coordinates of the corresponding point (0.6561, 0.7547) on the unit circle. The value of cos 49° is equal to the x-coordinate (0.6561). ∴ cos 49° = 0.6561.
What is the Value of Cos 49 Degrees in Terms of Sin 49°?
Using trigonometric identities, we can write cos 49° in terms of sin 49° as, cos(49°) = √(1 - sin²(49°)). Here, the value of sin 49° is equal to 0.7547.
How to Find Cos 49° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 49° can be given in terms of other trigonometric functions as:
- ± √(1-sin²(49°))
- ± 1/√(1 + tan²(49°))
- ± cot 49°/√(1 + cot²(49°))
- ± √(cosec²(49°) - 1)/cosec 49°
- 1/sec 49°
☛ Also check: trigonometric table