Cos 870 Degrees

The value of cos 870 degrees is -0.8660254. . .. Cos 870 degrees in radians is written as cos (870° × π/180°), i.e., cos (29π/6) or cos (15.184364. . .). In this article, we will discuss the methods to find the value of cos 870 degrees with examples.

• Cos 870°: -0.8660254. . .
• Cos 870° in fraction: −√3/2
• Cos (-870 degrees): -0.8660254. . .
• Cos 870° in radians: cos (29π/6) or cos (15.1843644 . . .)

What is the Value of Cos 870 Degrees?

The value of cos 870 degrees in decimal is -0.866025403. . .. Cos 870 degrees can also be expressed using the equivalent of the given angle (870 degrees) in radians (15.18436 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 870 degrees = 870° × (π/180°) rad = 29π/6 or 15.1843 . . .
∴ cos 870° = cos(15.1843) = −√3/2 or -0.8660254. . .

Explanation:

For cos 870°, the angle 870° > 360°. Given the periodic property of the cosine function, we can represent it as cos(870° mod 360°) = cos(150°). The angle 870°, coterminal to angle 150°, is located in the Second Quadrant(Quadrant II).
Since cosine function is negative in the 2nd quadrant, thus cos 870 degrees value = −√3/2 or -0.8660254. . .
Similarly, cos 870° can also be written as, cos 870 degrees = (870° + n × 360°), n ∈ Z.
⇒ cos 870° = cos 1230° = cos 1590°, and so on.
Note: Since, cosine is an even function, the value of cos(-870°) = cos(870°).

Methods to Find Value of Cos 870 Degrees

The cosine function is negative in the 2nd quadrant. The value of cos 870° is given as -0.86602. . .. We can find the value of cos 870 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 870 Degrees Using Unit Circle

To find the value of cos 870 degrees using the unit circle, represent 870° in the form (2 × 360°) + 150° [∵ 870°>360°] ∵ cosine is a periodic function, cos 870° = cos 150°.

• Rotate ‘r’ anticlockwise to form 150° or 870° angle with the positive x-axis.
• The cos of 870 degrees equals the x-coordinate(-0.866) of the point of intersection (-0.866, 0.5) of unit circle and r.

Hence the value of cos 870° = x = -0.866 (approx)

Cos 870° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 870 degrees as:

• ± √(1-sin²(870°))
• ± 1/√(1 + tan²(870°))
• ± cot 870°/√(1 + cot²(870°))
• ±√(cosec²(870°) - 1)/cosec 870°
• 1/sec 870°

Note: Since 870° lies in the 2nd Quadrant, the final value of cos 870° will be negative.

We can use trigonometric identities to represent cos 870° as,

• -cos(180° - 870°) = -cos(-690°)
• -cos(180° + 870°) = -cos 1050°
• sin(90° + 870°) = sin 960°
• sin(90° - 870°) = sin(-780°)

☛ Also Check:

• cos 135 degrees
• cos 40 degrees
• cos 30 degrees
• cos 100 degrees
• cos 25 degrees
• cos 630 degrees

FAQs on Cos 870 Degrees

What is Cos 870 Degrees?

Cos 870 degrees is the value of cosine trigonometric function for an angle equal to 870 degrees. The value of cos 870° is −√3/2 or -0.866 (approx)

How to Find the Value of Cos 870 Degrees?

The value of cos 870 degrees can be calculated by constructing an angle of 870° with the x-axis, and then finding the coordinates of the corresponding point (-0.866, 0.5) on the unit circle. The value of cos 870° is equal to the x-coordinate (-0.866). ∴ cos 870° = -0.866.

How to Find Cos 870° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 870° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(870°))
• ± 1/√(1 + tan²(870°))
• ± cot 870°/√(1 + cot²(870°))
• ± √(cosec²(870°) - 1)/cosec 870°
• 1/sec 870°

☛ Also check: trigonometric table

What is the Value of Cos 870 Degrees in Terms of Cot 870°?

We can represent the cosine function in terms of the cotangent function using trig identities, cos 870° can be written as cot 870°/√(1 + cot²(870°)). Here, the value of cot 870° is equal to -1.73205.

What is the Exact Value of cos 870 Degrees?

The exact value of cos 870 degrees can be given accurately up to 8 decimal places as -0.86602540 and −√3/2 in fraction.