Cos 52 Degrees
The value of cos 52 degrees is 0.6156614. . .. Cos 52 degrees in radians is written as cos (52° × π/180°), i.e., cos (13π/45) or cos (0.907571. . .). In this article, we will discuss the methods to find the value of cos 52 degrees with examples.
- Cos 52°: 0.6156614. . .
- Cos (-52 degrees): 0.6156614. . .
- Cos 52° in radians: cos (13π/45) or cos (0.9075712 . . .)
What is the Value of Cos 52 Degrees?
The value of cos 52 degrees in decimal is 0.615661475. . .. Cos 52 degrees can also be expressed using the equivalent of the given angle (52 degrees) in radians (0.90757 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 52 degrees = 52° × (π/180°) rad = 13π/45 or 0.9075 . . .
∴ cos 52° = cos(0.9075) = 0.6156614. . .
Explanation:
For cos 52 degrees, the angle 52° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 52° value = 0.6156614. . .
Since the cosine function is a periodic function, we can represent cos 52° as, cos 52 degrees = cos(52° + n × 360°), n ∈ Z.
⇒ cos 52° = cos 412° = cos 772°, and so on.
Note: Since, cosine is an even function, the value of cos(-52°) = cos(52°).
Methods to Find Value of Cos 52 Degrees
The cosine function is positive in the 1st quadrant. The value of cos 52° is given as 0.61566. . .. We can find the value of cos 52 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Cos 52° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 52 degrees as:
- ± √(1-sin²(52°))
- ± 1/√(1 + tan²(52°))
- ± cot 52°/√(1 + cot²(52°))
- ±√(cosec²(52°) - 1)/cosec 52°
- 1/sec 52°
Note: Since 52° lies in the 1st Quadrant, the final value of cos 52° will be positive.
We can use trigonometric identities to represent cos 52° as,
- -cos(180° - 52°) = -cos 128°
- -cos(180° + 52°) = -cos 232°
- sin(90° + 52°) = sin 142°
- sin(90° - 52°) = sin 38°
Cos 52 Degrees Using Unit Circle
To find the value of cos 52 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 52° angle with the positive x-axis.
- The cos of 52 degrees equals the x-coordinate(0.6157) of the point of intersection (0.6157, 0.788) of unit circle and r.
Hence the value of cos 52° = x = 0.6157 (approx)
☛ Also Check:
FAQs on Cos 52 Degrees
What is Cos 52 Degrees?
Cos 52 degrees is the value of cosine trigonometric function for an angle equal to 52 degrees. The value of cos 52° is 0.6157 (approx)
How to Find the Value of Cos 52 Degrees?
The value of cos 52 degrees can be calculated by constructing an angle of 52° with the x-axis, and then finding the coordinates of the corresponding point (0.6157, 0.788) on the unit circle. The value of cos 52° is equal to the x-coordinate (0.6157). ∴ cos 52° = 0.6157.
How to Find Cos 52° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 52° can be given in terms of other trigonometric functions as:
- ± √(1-sin²(52°))
- ± 1/√(1 + tan²(52°))
- ± cot 52°/√(1 + cot²(52°))
- ± √(cosec²(52°) - 1)/cosec 52°
- 1/sec 52°
☛ Also check: trigonometric table
What is the Value of Cos 52 Degrees in Terms of Tan 52°?
We know, using trig identities, we can write cos 52° as 1/√(1 + tan²(52°)). Here, the value of tan 52° is equal to 1.279941.
What is the Value of Cos 52° in Terms of Sec 52°?
Since the secant function is the reciprocal of the cosine function, we can write cos 52° as 1/sec(52°). The value of sec 52° is equal to 1.624269.