Cos 28 Degrees
The value of cos 28 degrees is 0.8829475. . .. Cos 28 degrees in radians is written as cos (28° × π/180°), i.e., cos (7π/45) or cos (0.488692. . .). In this article, we will discuss the methods to find the value of cos 28 degrees with examples.
- Cos 28°: 0.8829475. . .
- Cos (-28 degrees): 0.8829475. . .
- Cos 28° in radians: cos (7π/45) or cos (0.4886921 . . .)
What is the Value of Cos 28 Degrees?
The value of cos 28 degrees in decimal is 0.882947592. . .. Cos 28 degrees can also be expressed using the equivalent of the given angle (28 degrees) in radians (0.48869 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 28 degrees = 28° × (π/180°) rad = 7π/45 or 0.4886 . . .
∴ cos 28° = cos(0.4886) = 0.8829475. . .
Explanation:
For cos 28 degrees, the angle 28° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 28° value = 0.8829475. . .
Since the cosine function is a periodic function, we can represent cos 28° as, cos 28 degrees = cos(28° + n × 360°), n ∈ Z.
⇒ cos 28° = cos 388° = cos 748°, and so on.
Note: Since, cosine is an even function, the value of cos(-28°) = cos(28°).
Methods to Find Value of Cos 28 Degrees
The cosine function is positive in the 1st quadrant. The value of cos 28° is given as 0.88294. . .. We can find the value of cos 28 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Cos 28 Degrees Using Unit Circle
To find the value of cos 28 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 28° angle with the positive x-axis.
- The cos of 28 degrees equals the x-coordinate(0.8829) of the point of intersection (0.8829, 0.4695) of unit circle and r.
Hence the value of cos 28° = x = 0.8829 (approx)
Cos 28° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 28 degrees as:
- ± √(1-sin²(28°))
- ± 1/√(1 + tan²(28°))
- ± cot 28°/√(1 + cot²(28°))
- ±√(cosec²(28°) - 1)/cosec 28°
- 1/sec 28°
Note: Since 28° lies in the 1st Quadrant, the final value of cos 28° will be positive.
We can use trigonometric identities to represent cos 28° as,
- -cos(180° - 28°) = -cos 152°
- -cos(180° + 28°) = -cos 208°
- sin(90° + 28°) = sin 118°
- sin(90° - 28°) = sin 62°
☛ Also Check:
FAQs on Cos 28 Degrees
What is Cos 28 Degrees?
Cos 28 degrees is the value of cosine trigonometric function for an angle equal to 28 degrees. The value of cos 28° is 0.8829 (approx)
What is the Value of Cos 28 Degrees in Terms of Sin 28°?
Using trigonometric identities, we can write cos 28° in terms of sin 28° as, cos(28°) = √(1 - sin²(28°)). Here, the value of sin 28° is equal to 0.4695.
How to Find Cos 28° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 28° can be given in terms of other trigonometric functions as:
- ± √(1-sin²(28°))
- ± 1/√(1 + tan²(28°))
- ± cot 28°/√(1 + cot²(28°))
- ± √(cosec²(28°) - 1)/cosec 28°
- 1/sec 28°
☛ Also check: trigonometric table
What is the Value of Cos 28° in Terms of Sec 28°?
Since the secant function is the reciprocal of the cosine function, we can write cos 28° as 1/sec(28°). The value of sec 28° is equal to 1.132570.
How to Find the Value of Cos 28 Degrees?
The value of cos 28 degrees can be calculated by constructing an angle of 28° with the x-axis, and then finding the coordinates of the corresponding point (0.8829, 0.4695) on the unit circle. The value of cos 28° is equal to the x-coordinate (0.8829). ∴ cos 28° = 0.8829.