Cos 17 Degrees

The value of cos 17 degrees is 0.9563047. . .. Cos 17 degrees in radians is written as cos (17° × π/180°), i.e., cos (0.296705. . .). In this article, we will discuss the methods to find the value of cos 17 degrees with examples.

• Cos 17°: 0.9563047. . .
• Cos (-17 degrees): 0.9563047. . .
• Cos 17° in radians: cos (0.2967059 . . .)

What is the Value of Cos 17 Degrees?

The value of cos 17 degrees in decimal is 0.956304755. . .. Cos 17 degrees can also be expressed using the equivalent of the given angle (17 degrees) in radians (0.29670 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 17 degrees = 17° × (π/180°) rad = 0.2967 . . .
∴ cos 17° = cos(0.2967) = 0.9563047. . .

Explanation:

For cos 17 degrees, the angle 17° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 17° value = 0.9563047. . .
Since the cosine function is a periodic function, we can represent cos 17° as, cos 17 degrees = cos(17° + n × 360°), n ∈ Z.
⇒ cos 17° = cos 377° = cos 737°, and so on.
Note: Since, cosine is an even function, the value of cos(-17°) = cos(17°).

Methods to Find Value of Cos 17 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 17° is given as 0.95630. . .. We can find the value of cos 17 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 17 Degrees Using Unit Circle

To find the value of cos 17 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 17° angle with the positive x-axis.
• The cos of 17 degrees equals the x-coordinate(0.9563) of the point of intersection (0.9563, 0.2924) of unit circle and r.

Hence the value of cos 17° = x = 0.9563 (approx)

Cos 17° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 17 degrees as:

• ± √(1-sin²(17°))
• ± 1/√(1 + tan²(17°))
• ± cot 17°/√(1 + cot²(17°))
• ±√(cosec²(17°) - 1)/cosec 17°
• 1/sec 17°

Note: Since 17° lies in the 1st Quadrant, the final value of cos 17° will be positive.

We can use trigonometric identities to represent cos 17° as,

• -cos(180° - 17°) = -cos 163°
• -cos(180° + 17°) = -cos 197°
• sin(90° + 17°) = sin 107°
• sin(90° - 17°) = sin 73°

☛ Also Check:

• cos 2 degrees
• cos 20 degrees
• cos 240 degrees
• cos 76 degrees
• cos 19 degrees
• cos 56 degrees

FAQs on Cos 17 Degrees

What is Cos 17 Degrees?

Cos 17 degrees is the value of cosine trigonometric function for an angle equal to 17 degrees. The value of cos 17° is 0.9563 (approx)

How to Find the Value of Cos 17 Degrees?

The value of cos 17 degrees can be calculated by constructing an angle of 17° with the x-axis, and then finding the coordinates of the corresponding point (0.9563, 0.2924) on the unit circle. The value of cos 17° is equal to the x-coordinate (0.9563). ∴ cos 17° = 0.9563.

What is the Exact Value of cos 17 Degrees?

The exact value of cos 17 degrees can be given accurately up to 8 decimal places as 0.95630475.

What is the Value of Cos 17 Degrees in Terms of Sin 17°?

Using trigonometric identities, we can write cos 17° in terms of sin 17° as, cos(17°) = √(1 - sin²(17°)). Here, the value of sin 17° is equal to 0.2924.

How to Find Cos 17° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 17° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(17°))
• ± 1/√(1 + tan²(17°))
• ± cot 17°/√(1 + cot²(17°))
• ± √(cosec²(17°) - 1)/cosec 17°
• 1/sec 17°

☛ Also check: trigonometry table