Cos 69 Degrees

The value of cos 69 degrees is 0.3583679. . .. Cos 69 degrees in radians is written as cos (69° × π/180°), i.e., cos (23π/60) or cos (1.204277. . .). In this article, we will discuss the methods to find the value of cos 69 degrees with examples.

• Cos 69°: 0.3583679. . .
• Cos (-69 degrees): 0.3583679. . .
• Cos 69° in radians: cos (23π/60) or cos (1.2042771 . . .)

What is the Value of Cos 69 Degrees?

The value of cos 69 degrees in decimal is 0.358367949. . .. Cos 69 degrees can also be expressed using the equivalent of the given angle (69 degrees) in radians (1.20427 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 69 degrees = 69° × (π/180°) rad = 23π/60 or 1.2042 . . .
∴ cos 69° = cos(1.2042) = 0.3583679. . .

Explanation:

For cos 69 degrees, the angle 69° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 69° value = 0.3583679. . .
Since the cosine function is a periodic function, we can represent cos 69° as, cos 69 degrees = cos(69° + n × 360°), n ∈ Z.
⇒ cos 69° = cos 429° = cos 789°, and so on.
Note: Since, cosine is an even function, the value of cos(-69°) = cos(69°).

Methods to Find Value of Cos 69 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 69° is given as 0.35836. . .. We can find the value of cos 69 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 69° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 69 degrees as:

• ± √(1-sin²(69°))
• ± 1/√(1 + tan²(69°))
• ± cot 69°/√(1 + cot²(69°))
• ±√(cosec²(69°) - 1)/cosec 69°
• 1/sec 69°

Note: Since 69° lies in the 1st Quadrant, the final value of cos 69° will be positive.

We can use trigonometric identities to represent cos 69° as,

• -cos(180° - 69°) = -cos 111°
• -cos(180° + 69°) = -cos 249°
• sin(90° + 69°) = sin 159°
• sin(90° - 69°) = sin 21°

Cos 69 Degrees Using Unit Circle

To find the value of cos 69 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 69° angle with the positive x-axis.
• The cos of 69 degrees equals the x-coordinate(0.3584) of the point of intersection (0.3584, 0.9336) of unit circle and r.

Hence the value of cos 69° = x = 0.3584 (approx)

☛ Also Check:

• cos 150 degrees
• cos 60 degrees
• cos 18 degrees
• cos 630 degrees
• cos 69 degrees
• cos 250 degrees

FAQs on Cos 69 Degrees

What is Cos 69 Degrees?

Cos 69 degrees is the value of cosine trigonometric function for an angle equal to 69 degrees. The value of cos 69° is 0.3584 (approx)

How to Find Cos 69° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 69° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(69°))
• ± 1/√(1 + tan²(69°))
• ± cot 69°/√(1 + cot²(69°))
• ± √(cosec²(69°) - 1)/cosec 69°
• 1/sec 69°

☛ Also check: trigonometric table

What is the Value of Cos 69 Degrees in Terms of Cot 69°?

We can represent the cosine function in terms of the cotangent function using trig identities, cos 69° can be written as cot 69°/√(1 + cot²(69°)). Here, the value of cot 69° is equal to 0.38386.

What is the Value of Cos 69° in Terms of Cosec 69°?

Since the cosine function can be represented using the cosecant function, we can write cos 69° as [√(cosec²(69°) - 1)/cosec 69°]. The value of cosec 69° is equal to 1.07114.

How to Find the Value of Cos 69 Degrees?

The value of cos 69 degrees can be calculated by constructing an angle of 69° with the x-axis, and then finding the coordinates of the corresponding point (0.3584, 0.9336) on the unit circle. The value of cos 69° is equal to the x-coordinate (0.3584). ∴ cos 69° = 0.3584.