Cos 170 Degrees
The value of cos 170 degrees is -0.9848077. . .. Cos 170 degrees in radians is written as cos (170° × π/180°), i.e., cos (17π/18) or cos (2.967059. . .). In this article, we will discuss the methods to find the value of cos 170 degrees with examples.
- Cos 170°: -0.9848077. . .
- Cos (-170 degrees): -0.9848077. . .
- Cos 170° in radians: cos (17π/18) or cos (2.9670597 . . .)
What is the Value of Cos 170 Degrees?
The value of cos 170 degrees in decimal is -0.984807753. . .. Cos 170 degrees can also be expressed using the equivalent of the given angle (170 degrees) in radians (2.96705 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 170 degrees = 170° × (π/180°) rad = 17π/18 or 2.9670 . . .
∴ cos 170° = cos(2.9670) = -0.9848077. . .
Explanation:
For cos 170 degrees, the angle 170° lies between 90° and 180° (Second Quadrant). Since cosine function is negative in the second quadrant, thus cos 170° value = -0.9848077. . .
Since the cosine function is a periodic function, we can represent cos 170° as, cos 170 degrees = cos(170° + n × 360°), n ∈ Z.
⇒ cos 170° = cos 530° = cos 890°, and so on.
Note: Since, cosine is an even function, the value of cos(-170°) = cos(170°).
Methods to Find Value of Cos 170 Degrees
The cosine function is negative in the 2nd quadrant. The value of cos 170° is given as -0.98480. . .. We can find the value of cos 170 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Cos 170° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 170 degrees as:
- ± √(1-sin²(170°))
- ± 1/√(1 + tan²(170°))
- ± cot 170°/√(1 + cot²(170°))
- ±√(cosec²(170°) - 1)/cosec 170°
- 1/sec 170°
Note: Since 170° lies in the 2nd Quadrant, the final value of cos 170° will be negative.
We can use trigonometric identities to represent cos 170° as,
- -cos(180° - 170°) = -cos 10°
- -cos(180° + 170°) = -cos 350°
- sin(90° + 170°) = sin 260°
- sin(90° - 170°) = sin(-80°)
Cos 170 Degrees Using Unit Circle
To find the value of cos 170 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 170° angle with the positive x-axis.
- The cos of 170 degrees equals the x-coordinate(-0.9848) of the point of intersection (-0.9848, 0.1736) of unit circle and r.
Hence the value of cos 170° = x = -0.9848 (approx)
☛ Also Check:
FAQs on Cos 170 Degrees
What is Cos 170 Degrees?
Cos 170 degrees is the value of cosine trigonometric function for an angle equal to 170 degrees. The value of cos 170° is -0.9848 (approx)
How to Find Cos 170° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 170° can be given in terms of other trigonometric functions as:
- ± √(1-sin²(170°))
- ± 1/√(1 + tan²(170°))
- ± cot 170°/√(1 + cot²(170°))
- ± √(cosec²(170°) - 1)/cosec 170°
- 1/sec 170°
☛ Also check: trigonometric table
What is the Value of Cos 170° in Terms of Sec 170°?
Since the secant function is the reciprocal of the cosine function, we can write cos 170° as 1/sec(170°). The value of sec 170° is equal to -1.015426.
What is the Value of Cos 170 Degrees in Terms of Sin 170°?
Using trigonometric identities, we can write cos 170° in terms of sin 170° as, cos(170°) = -√(1 - sin²(170°)). Here, the value of sin 170° is equal to 0.1736.
How to Find the Value of Cos 170 Degrees?
The value of cos 170 degrees can be calculated by constructing an angle of 170° with the x-axis, and then finding the coordinates of the corresponding point (-0.9848, 0.1736) on the unit circle. The value of cos 170° is equal to the x-coordinate (-0.9848). ∴ cos 170° = -0.9848.