Cos 217 Degrees

The value of cos 217 degrees is -0.7986355. . .. Cos 217 degrees in radians is written as cos (217° × π/180°), i.e., cos (3.787364. . .). In this article, we will discuss the methods to find the value of cos 217 degrees with examples.

• Cos 217°: -0.7986355. . .
• Cos (-217 degrees): -0.7986355. . .
• Cos 217° in radians: cos (3.7873644 . . .)

What is the Value of Cos 217 Degrees?

The value of cos 217 degrees in decimal is -0.798635510. . .. Cos 217 degrees can also be expressed using the equivalent of the given angle (217 degrees) in radians (3.78736 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 217 degrees = 217° × (π/180°) rad = 3.7873 . . .
∴ cos 217° = cos(3.7873) = -0.7986355. . .

Explanation:

For cos 217 degrees, the angle 217° lies between 180° and 270° (Third Quadrant). Since cosine function is negative in the third quadrant, thus cos 217° value = -0.7986355. . .
Since the cosine function is a periodic function, we can represent cos 217° as, cos 217 degrees = cos(217° + n × 360°), n ∈ Z.
⇒ cos 217° = cos 577° = cos 937°, and so on.
Note: Since, cosine is an even function, the value of cos(-217°) = cos(217°).

Methods to Find Value of Cos 217 Degrees

The cosine function is negative in the 3rd quadrant. The value of cos 217° is given as -0.79863. . .. We can find the value of cos 217 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 217° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 217 degrees as:

• ± √(1-sin²(217°))
• ± 1/√(1 + tan²(217°))
• ± cot 217°/√(1 + cot²(217°))
• ±√(cosec²(217°) - 1)/cosec 217°
• 1/sec 217°

Note: Since 217° lies in the 3rd Quadrant, the final value of cos 217° will be negative.

We can use trigonometric identities to represent cos 217° as,

• -cos(180° - 217°) = -cos(-37°)
• -cos(180° + 217°) = -cos 397°
• sin(90° + 217°) = sin 307°
• sin(90° - 217°) = sin(-127°)

Cos 217 Degrees Using Unit Circle

To find the value of cos 217 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 217° angle with the positive x-axis.
• The cos of 217 degrees equals the x-coordinate(-0.7986) of the point of intersection (-0.7986, -0.6018) of unit circle and r.

Hence the value of cos 217° = x = -0.7986 (approx)

☛ Also Check:

• cos 120 degrees
• cos 225 degrees
• cos 1 degrees
• cos 54 degrees
• cos 79 degrees
• cos 5 degrees

FAQs on Cos 217 Degrees

What is Cos 217 Degrees?

Cos 217 degrees is the value of cosine trigonometric function for an angle equal to 217 degrees. The value of cos 217° is -0.7986 (approx)

How to Find the Value of Cos 217 Degrees?

The value of cos 217 degrees can be calculated by constructing an angle of 217° with the x-axis, and then finding the coordinates of the corresponding point (-0.7986, -0.6018) on the unit circle. The value of cos 217° is equal to the x-coordinate (-0.7986). ∴ cos 217° = -0.7986.

What is the Value of Cos 217 Degrees in Terms of Sin 217°?

Using trigonometric identities, we can write cos 217° in terms of sin 217° as, cos(217°) = -√(1 - sin²(217°)). Here, the value of sin 217° is equal to -0.6018.

How to Find Cos 217° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 217° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(217°))
• ± 1/√(1 + tan²(217°))
• ± cot 217°/√(1 + cot²(217°))
• ± √(cosec²(217°) - 1)/cosec 217°
• 1/sec 217°

☛ Also check: trigonometric table

What is the Value of Cos 217° in Terms of Cosec 217°?

Since the cosine function can be represented using the cosecant function, we can write cos 217° as [√(cosec²(217°) - 1)/cosec 217°]. The value of cosec 217° is equal to -1.66164.