Cos 74 Degrees
The value of cos 74 degrees is 0.2756373. . .. Cos 74 degrees in radians is written as cos (74° × π/180°), i.e., cos (37π/90) or cos (1.291543. . .). In this article, we will discuss the methods to find the value of cos 74 degrees with examples.
- Cos 74°: 0.2756373. . .
- Cos (-74 degrees): 0.2756373. . .
- Cos 74° in radians: cos (37π/90) or cos (1.2915436 . . .)
What is the Value of Cos 74 Degrees?
The value of cos 74 degrees in decimal is 0.275637355. . .. Cos 74 degrees can also be expressed using the equivalent of the given angle (74 degrees) in radians (1.29154 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 74 degrees = 74° × (π/180°) rad = 37π/90 or 1.2915 . . .
∴ cos 74° = cos(1.2915) = 0.2756373. . .
Explanation:
For cos 74 degrees, the angle 74° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 74° value = 0.2756373. . .
Since the cosine function is a periodic function, we can represent cos 74° as, cos 74 degrees = cos(74° + n × 360°), n ∈ Z.
⇒ cos 74° = cos 434° = cos 794°, and so on.
Note: Since, cosine is an even function, the value of cos(-74°) = cos(74°).
Methods to Find Value of Cos 74 Degrees
The cosine function is positive in the 1st quadrant. The value of cos 74° is given as 0.27563. . .. We can find the value of cos 74 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Cos 74° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 74 degrees as:
- ± √(1-sin²(74°))
- ± 1/√(1 + tan²(74°))
- ± cot 74°/√(1 + cot²(74°))
- ±√(cosec²(74°) - 1)/cosec 74°
- 1/sec 74°
Note: Since 74° lies in the 1st Quadrant, the final value of cos 74° will be positive.
We can use trigonometric identities to represent cos 74° as,
- -cos(180° - 74°) = -cos 106°
- -cos(180° + 74°) = -cos 254°
- sin(90° + 74°) = sin 164°
- sin(90° - 74°) = sin 16°
Cos 74 Degrees Using Unit Circle
To find the value of cos 74 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 74° angle with the positive x-axis.
- The cos of 74 degrees equals the x-coordinate(0.2756) of the point of intersection (0.2756, 0.9613) of unit circle and r.
Hence the value of cos 74° = x = 0.2756 (approx)
☛ Also Check:
FAQs on Cos 74 Degrees
What is Cos 74 Degrees?
Cos 74 degrees is the value of cosine trigonometric function for an angle equal to 74 degrees. The value of cos 74° is 0.2756 (approx)
How to Find the Value of Cos 74 Degrees?
The value of cos 74 degrees can be calculated by constructing an angle of 74° with the x-axis, and then finding the coordinates of the corresponding point (0.2756, 0.9613) on the unit circle. The value of cos 74° is equal to the x-coordinate (0.2756). ∴ cos 74° = 0.2756.
What is the Value of Cos 74 Degrees in Terms of Tan 74°?
We know, using trig identities, we can write cos 74° as 1/√(1 + tan²(74°)). Here, the value of tan 74° is equal to 3.487414.
What is the Exact Value of cos 74 Degrees?
The exact value of cos 74 degrees can be given accurately up to 8 decimal places as 0.27563735.
How to Find Cos 74° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 74° can be given in terms of other trigonometric functions as:
- ± √(1-sin²(74°))
- ± 1/√(1 + tan²(74°))
- ± cot 74°/√(1 + cot²(74°))
- ± √(cosec²(74°) - 1)/cosec 74°
- 1/sec 74°
☛ Also check: trigonometry table