Cos 26 Degrees

The value of cos 26 degrees is 0.8987940. . .. Cos 26 degrees in radians is written as cos (26° × π/180°), i.e., cos (13π/90) or cos (0.453785. . .). In this article, we will discuss the methods to find the value of cos 26 degrees with examples.

• Cos 26°: 0.8987940. . .
• Cos (-26 degrees): 0.8987940. . .
• Cos 26° in radians: cos (13π/90) or cos (0.4537856 . . .)

What is the Value of Cos 26 Degrees?

The value of cos 26 degrees in decimal is 0.898794046. . .. Cos 26 degrees can also be expressed using the equivalent of the given angle (26 degrees) in radians (0.45378 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 26 degrees = 26° × (π/180°) rad = 13π/90 or 0.4537 . . .
∴ cos 26° = cos(0.4537) = 0.8987940. . .

Explanation:

For cos 26 degrees, the angle 26° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 26° value = 0.8987940. . .
Since the cosine function is a periodic function, we can represent cos 26° as, cos 26 degrees = cos(26° + n × 360°), n ∈ Z.
⇒ cos 26° = cos 386° = cos 746°, and so on.
Note: Since, cosine is an even function, the value of cos(-26°) = cos(26°).

Methods to Find Value of Cos 26 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 26° is given as 0.89879. . .. We can find the value of cos 26 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 26 Degrees Using Unit Circle

To find the value of cos 26 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 26° angle with the positive x-axis.
• The cos of 26 degrees equals the x-coordinate(0.8988) of the point of intersection (0.8988, 0.4384) of unit circle and r.

Hence the value of cos 26° = x = 0.8988 (approx)

Cos 26° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 26 degrees as:

• ± √(1-sin²(26°))
• ± 1/√(1 + tan²(26°))
• ± cot 26°/√(1 + cot²(26°))
• ±√(cosec²(26°) - 1)/cosec 26°
• 1/sec 26°

Note: Since 26° lies in the 1st Quadrant, the final value of cos 26° will be positive.

We can use trigonometric identities to represent cos 26° as,

• -cos(180° - 26°) = -cos 154°
• -cos(180° + 26°) = -cos 206°
• sin(90° + 26°) = sin 116°
• sin(90° - 26°) = sin 64°

☛ Also Check:

• cos 36 degrees
• cos 150 degrees
• cos 18 degrees
• cos 32 degrees
• cos 26 degrees
• cos 95 degrees

FAQs on Cos 26 Degrees

What is Cos 26 Degrees?

Cos 26 degrees is the value of cosine trigonometric function for an angle equal to 26 degrees. The value of cos 26° is 0.8988 (approx)

What is the Exact Value of cos 26 Degrees?

The exact value of cos 26 degrees can be given accurately up to 8 decimal places as 0.89879404.

How to Find the Value of Cos 26 Degrees?

The value of cos 26 degrees can be calculated by constructing an angle of 26° with the x-axis, and then finding the coordinates of the corresponding point (0.8988, 0.4384) on the unit circle. The value of cos 26° is equal to the x-coordinate (0.8988). ∴ cos 26° = 0.8988.

How to Find Cos 26° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 26° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(26°))
• ± 1/√(1 + tan²(26°))
• ± cot 26°/√(1 + cot²(26°))
• ± √(cosec²(26°) - 1)/cosec 26°
• 1/sec 26°

☛ Also check: trigonometry table

What is the Value of Cos 26 Degrees in Terms of Cot 26°?

We can represent the cosine function in terms of the cotangent function using trig identities, cos 26° can be written as cot 26°/√(1 + cot²(26°)). Here, the value of cot 26° is equal to 2.05030.