Cos 35 Degrees

The value of cos 35 degrees is 0.8191520. . .. Cos 35 degrees in radians is written as cos (35° × π/180°), i.e., cos (7π/36) or cos (0.610865. . .). In this article, we will discuss the methods to find the value of cos 35 degrees with examples.

• Cos 35°: 0.8191520. . .
• Cos (-35 degrees): 0.8191520. . .
• Cos 35° in radians: cos (7π/36) or cos (0.6108652 . . .)

What is the Value of Cos 35 Degrees?

The value of cos 35 degrees in decimal is 0.819152044. . .. Cos 35 degrees can also be expressed using the equivalent of the given angle (35 degrees) in radians (0.61086 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 35 degrees = 35° × (π/180°) rad = 7π/36 or 0.6108 . . .
∴ cos 35° = cos(0.6108) = 0.8191520. . .

Explanation:

For cos 35 degrees, the angle 35° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 35° value = 0.8191520. . .
Since the cosine function is a periodic function, we can represent cos 35° as, cos 35 degrees = cos(35° + n × 360°), n ∈ Z.
⇒ cos 35° = cos 395° = cos 755°, and so on.
Note: Since, cosine is an even function, the value of cos(-35°) = cos(35°).

Methods to Find Value of Cos 35 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 35° is given as 0.81915. . .. We can find the value of cos 35 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 35 Degrees Using Unit Circle

To find the value of cos 35 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 35° angle with the positive x-axis.
• The cos of 35 degrees equals the x-coordinate(0.8192) of the point of intersection (0.8192, 0.5736) of unit circle and r.

Hence the value of cos 35° = x = 0.8192 (approx)

Cos 35° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 35 degrees as:

• ± √(1-sin²(35°))
• ± 1/√(1 + tan²(35°))
• ± cot 35°/√(1 + cot²(35°))
• ±√(cosec²(35°) - 1)/cosec 35°
• 1/sec 35°

Note: Since 35° lies in the 1st Quadrant, the final value of cos 35° will be positive.

We can use trigonometric identities to represent cos 35° as,

• -cos(180° - 35°) = -cos 145°
• -cos(180° + 35°) = -cos 215°
• sin(90° + 35°) = sin 125°
• sin(90° - 35°) = sin 55°

☛ Also Check:

• cos 240 degrees
• cos 360 degrees
• cos 10 degrees
• cos 31 degrees
• cos 155 degrees
• cos 27 degrees

FAQs on Cos 35 Degrees

What is Cos 35 Degrees?

Cos 35 degrees is the value of cosine trigonometric function for an angle equal to 35 degrees. The value of cos 35° is 0.8192 (approx)

How to Find Cos 35° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 35° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(35°))
• ± 1/√(1 + tan²(35°))
• ± cot 35°/√(1 + cot²(35°))
• ± √(cosec²(35°) - 1)/cosec 35°
• 1/sec 35°

☛ Also check: trigonometry table

How to Find the Value of Cos 35 Degrees?

The value of cos 35 degrees can be calculated by constructing an angle of 35° with the x-axis, and then finding the coordinates of the corresponding point (0.8192, 0.5736) on the unit circle. The value of cos 35° is equal to the x-coordinate (0.8192). ∴ cos 35° = 0.8192.

What is the Value of Cos 35° in Terms of Sec 35°?

Since the secant function is the reciprocal of the cosine function, we can write cos 35° as 1/sec(35°). The value of sec 35° is equal to 1.220774.

What is the Value of Cos 35 Degrees in Terms of Cot 35°?

We can represent the cosine function in terms of the cotangent function using trig identities, cos 35° can be written as cot 35°/√(1 + cot²(35°)). Here, the value of cot 35° is equal to 1.42814.