Cos 89 Degrees

The value of cos 89 degrees is 0.0174524. . .. Cos 89 degrees in radians is written as cos (89° × π/180°), i.e., cos (1.553343. . .). In this article, we will discuss the methods to find the value of cos 89 degrees with examples.

• Cos 89°: 0.0174524. . .
• Cos (-89 degrees): 0.0174524. . .
• Cos 89° in radians: cos (1.5533430 . . .)

What is the Value of Cos 89 Degrees?

The value of cos 89 degrees in decimal is 0.017452406. . .. Cos 89 degrees can also be expressed using the equivalent of the given angle (89 degrees) in radians (1.55334 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 89 degrees = 89° × (π/180°) rad = 1.5533 . . .
∴ cos 89° = cos(1.5533) = 0.0174524. . .

Explanation:

For cos 89 degrees, the angle 89° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 89° value = 0.0174524. . .
Since the cosine function is a periodic function, we can represent cos 89° as, cos 89 degrees = cos(89° + n × 360°), n ∈ Z.
⇒ cos 89° = cos 449° = cos 809°, and so on.
Note: Since, cosine is an even function, the value of cos(-89°) = cos(89°).

Methods to Find Value of Cos 89 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 89° is given as 0.01745. . .. We can find the value of cos 89 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 89° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 89 degrees as:

• ± √(1-sin²(89°))
• ± 1/√(1 + tan²(89°))
• ± cot 89°/√(1 + cot²(89°))
• ±√(cosec²(89°) - 1)/cosec 89°
• 1/sec 89°

Note: Since 89° lies in the 1st Quadrant, the final value of cos 89° will be positive.

We can use trigonometric identities to represent cos 89° as,

• -cos(180° - 89°) = -cos 91°
• -cos(180° + 89°) = -cos 269°
• sin(90° + 89°) = sin 179°
• sin(90° - 89°) = sin 1°

Cos 89 Degrees Using Unit Circle

To find the value of cos 89 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 89° angle with the positive x-axis.
• The cos of 89 degrees equals the x-coordinate(0.0175) of the point of intersection (0.0175, 0.9998) of unit circle and r.

Hence the value of cos 89° = x = 0.0175 (approx)

☛ Also Check:

• cos 20 degrees
• cos 120 degrees
• cos 150 degrees
• cos 72 degrees
• cos 340 degrees
• cos 74 degrees

FAQs on Cos 89 Degrees

What is Cos 89 Degrees?

Cos 89 degrees is the value of cosine trigonometric function for an angle equal to 89 degrees. The value of cos 89° is 0.0175 (approx)

How to Find Cos 89° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 89° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(89°))
• ± 1/√(1 + tan²(89°))
• ± cot 89°/√(1 + cot²(89°))
• ± √(cosec²(89°) - 1)/cosec 89°
• 1/sec 89°

☛ Also check: trigonometry table

What is the Value of Cos 89 Degrees in Terms of Cot 89°?

We can represent the cosine function in terms of the cotangent function using trig identities, cos 89° can be written as cot 89°/√(1 + cot²(89°)). Here, the value of cot 89° is equal to 0.01745.

How to Find the Value of Cos 89 Degrees?

The value of cos 89 degrees can be calculated by constructing an angle of 89° with the x-axis, and then finding the coordinates of the corresponding point (0.0175, 0.9998) on the unit circle. The value of cos 89° is equal to the x-coordinate (0.0175). ∴ cos 89° = 0.0175.

What is the Exact Value of cos 89 Degrees?

The exact value of cos 89 degrees can be given accurately up to 8 decimal places as 0.01745240.