Cos 15 Degrees

The value of cos 15 degrees is 0.9659258. . .. Cos 15 degrees in radians is written as cos (15° × π/180°), i.e., cos (π/12) or cos (0.261799. . .). In this article, we will discuss the methods to find the value of cos 15 degrees with examples.

• Cos 15°: 0.9659258. . .
• Cos 15° in fraction: (√6 + √2)/4
• Cos (-15 degrees): 0.9659258. . .
• Cos 15° in radians: cos (π/12) or cos (0.2617993 . . .)

What is the Value of Cos 15 Degrees?

The value of cos 15 degrees in decimal is 0.965925826. . .. Cos 15 degrees can also be expressed using the equivalent of the given angle (15 degrees) in radians (0.26179 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 15 degrees = 15° × (π/180°) rad = π/12 or 0.2617 . . .
∴ cos 15° = cos(0.2617) = (√6 + √2)/4 or 0.9659258. . .

Explanation:

For cos 15 degrees, the angle 15° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 15° value = (√6 + √2)/4 or 0.9659258. . .
Since the cosine function is a periodic function, we can represent cos 15° as, cos 15 degrees = cos(15° + n × 360°), n ∈ Z.
⇒ cos 15° = cos 375° = cos 735°, and so on.
Note: Since, cosine is an even function, the value of cos(-15°) = cos(15°).

Methods to Find Value of Cos 15 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 15° is given as 0.96592. . .. We can find the value of cos 15 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 15 Degrees Using Unit Circle

To find the value of cos 15 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 15° angle with the positive x-axis.
• The cos of 15 degrees equals the x-coordinate(0.9659) of the point of intersection (0.9659, 0.2588) of unit circle and r.

Hence the value of cos 15° = x = 0.9659 (approx)

Cos 15° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 15 degrees as:

• ± √(1-sin²(15°))
• ± 1/√(1 + tan²(15°))
• ± cot 15°/√(1 + cot²(15°))
• ±√(cosec²(15°) - 1)/cosec 15°
• 1/sec 15°

Note: Since 15° lies in the 1st Quadrant, the final value of cos 15° will be positive.

We can use trigonometric identities to represent cos 15° as,

• -cos(180° - 15°) = -cos 165°
• -cos(180° + 15°) = -cos 195°
• sin(90° + 15°) = sin 105°
• sin(90° - 15°) = sin 75°

☛ Also Check:

• cos 45 degrees
• cos 90 degrees
• cos 150 degrees
• cos 140 degrees
• cos 144 degrees
• cos 720 degrees

FAQs on Cos 15 Degrees

What is Cos 15 Degrees?

Cos 15 degrees is the value of cosine trigonometric function for an angle equal to 15 degrees. The value of cos 15° is (√6 + √2)/4 or 0.9659 (approx)

What is the Value of Cos 15° in Terms of Sec 15°?

Since the secant function is the reciprocal of the cosine function, we can write cos 15° as 1/sec(15°). The value of sec 15° is equal to 1.035276.

How to Find Cos 15° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 15° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(15°))
• ± 1/√(1 + tan²(15°))
• ± cot 15°/√(1 + cot²(15°))
• ± √(cosec²(15°) - 1)/cosec 15°
• 1/sec 15°

☛ Also check: trigonometry table

What is the Value of Cos 15 Degrees in Terms of Sin 15°?

Using trigonometric identities, we can write cos 15° in terms of sin 15° as, cos(15°) = √(1 - sin²(15°)). Here, the value of sin 15° is equal to (√6 - √2)/4.

How to Find the Value of Cos 15 Degrees?

The value of cos 15 degrees can be calculated by constructing an angle of 15° with the x-axis, and then finding the coordinates of the corresponding point (0.9659, 0.2588) on the unit circle. The value of cos 15° is equal to the x-coordinate (0.9659). ∴ cos 15° = 0.9659.