Cos 87 Degrees
The value of cos 87 degrees is 0.0523359. . .. Cos 87 degrees in radians is written as cos (87° × π/180°), i.e., cos (29π/60) or cos (1.518436. . .). In this article, we will discuss the methods to find the value of cos 87 degrees with examples.
- Cos 87°: 0.0523359. . .
- Cos (-87 degrees): 0.0523359. . .
- Cos 87° in radians: cos (29π/60) or cos (1.5184364 . . .)
What is the Value of Cos 87 Degrees?
The value of cos 87 degrees in decimal is 0.052335956. . .. Cos 87 degrees can also be expressed using the equivalent of the given angle (87 degrees) in radians (1.51843 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 87 degrees = 87° × (π/180°) rad = 29π/60 or 1.5184 . . .
∴ cos 87° = cos(1.5184) = 0.0523359. . .
Explanation:
For cos 87 degrees, the angle 87° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 87° value = 0.0523359. . .
Since the cosine function is a periodic function, we can represent cos 87° as, cos 87 degrees = cos(87° + n × 360°), n ∈ Z.
⇒ cos 87° = cos 447° = cos 807°, and so on.
Note: Since, cosine is an even function, the value of cos(-87°) = cos(87°).
Methods to Find Value of Cos 87 Degrees
The cosine function is positive in the 1st quadrant. The value of cos 87° is given as 0.05233. . .. We can find the value of cos 87 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Cos 87° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 87 degrees as:
- ± √(1-sin²(87°))
- ± 1/√(1 + tan²(87°))
- ± cot 87°/√(1 + cot²(87°))
- ±√(cosec²(87°) - 1)/cosec 87°
- 1/sec 87°
Note: Since 87° lies in the 1st Quadrant, the final value of cos 87° will be positive.
We can use trigonometric identities to represent cos 87° as,
- -cos(180° - 87°) = -cos 93°
- -cos(180° + 87°) = -cos 267°
- sin(90° + 87°) = sin 177°
- sin(90° - 87°) = sin 3°
Cos 87 Degrees Using Unit Circle
To find the value of cos 87 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 87° angle with the positive x-axis.
- The cos of 87 degrees equals the x-coordinate(0.0523) of the point of intersection (0.0523, 0.9986) of unit circle and r.
Hence the value of cos 87° = x = 0.0523 (approx)
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FAQs on Cos 87 Degrees
What is Cos 87 Degrees?
Cos 87 degrees is the value of cosine trigonometric function for an angle equal to 87 degrees. The value of cos 87° is 0.0523 (approx)
What is the Value of Cos 87° in Terms of Cosec 87°?
Since the cosine function can be represented using the cosecant function, we can write cos 87° as [√(cosec²(87°) - 1)/cosec 87°]. The value of cosec 87° is equal to 1.00137.
How to Find the Value of Cos 87 Degrees?
The value of cos 87 degrees can be calculated by constructing an angle of 87° with the x-axis, and then finding the coordinates of the corresponding point (0.0523, 0.9986) on the unit circle. The value of cos 87° is equal to the x-coordinate (0.0523). ∴ cos 87° = 0.0523.
What is the Value of Cos 87 Degrees in Terms of Cot 87°?
We can represent the cosine function in terms of the cotangent function using trig identities, cos 87° can be written as cot 87°/√(1 + cot²(87°)). Here, the value of cot 87° is equal to 0.05240.
How to Find Cos 87° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 87° can be given in terms of other trigonometric functions as:
- ± √(1-sin²(87°))
- ± 1/√(1 + tan²(87°))
- ± cot 87°/√(1 + cot²(87°))
- ± √(cosec²(87°) - 1)/cosec 87°
- 1/sec 87°
☛ Also check: trigonometry table