Cos 95 Degrees

The value of cos 95 degrees is -0.0871557. . .. Cos 95 degrees in radians is written as cos (95° × π/180°), i.e., cos (19π/36) or cos (1.658062. . .). In this article, we will discuss the methods to find the value of cos 95 degrees with examples.

• Cos 95°: -0.0871557. . .
• Cos (-95 degrees): -0.0871557. . .
• Cos 95° in radians: cos (19π/36) or cos (1.6580627 . . .)

What is the Value of Cos 95 Degrees?

The value of cos 95 degrees in decimal is -0.087155742. . .. Cos 95 degrees can also be expressed using the equivalent of the given angle (95 degrees) in radians (1.65806 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 95 degrees = 95° × (π/180°) rad = 19π/36 or 1.6580 . . .
∴ cos 95° = cos(1.6580) = -0.0871557. . .

Explanation:

For cos 95 degrees, the angle 95° lies between 90° and 180° (Second Quadrant). Since cosine function is negative in the second quadrant, thus cos 95° value = -0.0871557. . .
Since the cosine function is a periodic function, we can represent cos 95° as, cos 95 degrees = cos(95° + n × 360°), n ∈ Z.
⇒ cos 95° = cos 455° = cos 815°, and so on.
Note: Since, cosine is an even function, the value of cos(-95°) = cos(95°).

Methods to Find Value of Cos 95 Degrees

The cosine function is negative in the 2nd quadrant. The value of cos 95° is given as -0.08715. . .. We can find the value of cos 95 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 95 Degrees Using Unit Circle

To find the value of cos 95 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 95° angle with the positive x-axis.
• The cos of 95 degrees equals the x-coordinate(-0.0872) of the point of intersection (-0.0872, 0.9962) of unit circle and r.

Hence the value of cos 95° = x = -0.0872 (approx)

Cos 95° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 95 degrees as:

• ± √(1-sin²(95°))
• ± 1/√(1 + tan²(95°))
• ± cot 95°/√(1 + cot²(95°))
• ±√(cosec²(95°) - 1)/cosec 95°
• 1/sec 95°

Note: Since 95° lies in the 2nd Quadrant, the final value of cos 95° will be negative.

We can use trigonometric identities to represent cos 95° as,

• -cos(180° - 95°) = -cos 85°
• -cos(180° + 95°) = -cos 275°
• sin(90° + 95°) = sin 185°
• sin(90° - 95°) = sin(-5°)

☛ Also Check:

• cos 0 degrees
• cos 36 degrees
• cos 270 degrees
• cos 480 degrees
• cos 110 degrees
• cos 170 degrees

FAQs on Cos 95 Degrees

What is Cos 95 Degrees?

Cos 95 degrees is the value of cosine trigonometric function for an angle equal to 95 degrees. The value of cos 95° is -0.0872 (approx)

What is the Value of Cos 95° in Terms of Cosec 95°?

Since the cosine function can be represented using the cosecant function, we can write cos 95° as -[√(cosec²(95°) - 1)/cosec 95°]. The value of cosec 95° is equal to 1.00381.

How to Find the Value of Cos 95 Degrees?

The value of cos 95 degrees can be calculated by constructing an angle of 95° with the x-axis, and then finding the coordinates of the corresponding point (-0.0872, 0.9962) on the unit circle. The value of cos 95° is equal to the x-coordinate (-0.0872). ∴ cos 95° = -0.0872.

How to Find Cos 95° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 95° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(95°))
• ± 1/√(1 + tan²(95°))
• ± cot 95°/√(1 + cot²(95°))
• ± √(cosec²(95°) - 1)/cosec 95°
• 1/sec 95°

☛ Also check: trigonometric table

What is the Value of Cos 95 Degrees in Terms of Tan 95°?

We know, using trig identities, we can write cos 95° as -1/√(1 + tan²(95°)). Here, the value of tan 95° is equal to -11.430052.