Sin 95 Degrees

The value of sin 95 degrees is 0.9961946. . .. Sin 95 degrees in radians is written as sin (95° × π/180°), i.e., sin (19π/36) or sin (1.658062. . .). In this article, we will discuss the methods to find the value of sin 95 degrees with examples.

• Sin 95°: 0.9961946. . .
• Sin (-95 degrees): -0.9961946. . .
• Sin 95° in radians: sin (19π/36) or sin (1.6580627 . . .)

What is the Value of Sin 95 Degrees?

The value of sin 95 degrees in decimal is 0.996194698. . .. Sin 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 . . .
∴ sin 95° = sin(1.6580) = 0.9961946. . .

Explanation:

For sin 95 degrees, the angle 95° lies between 90° and 180° (Second Quadrant). Since sine function is positive in the second quadrant, thus sin 95° value = 0.9961946. . .
Since the sine function is a periodic function, we can represent sin 95° as, sin 95 degrees = sin(95° + n × 360°), n ∈ Z.
⇒ sin 95° = sin 455° = sin 815°, and so on.
Note: Since, sine is an odd function, the value of sin(-95°) = -sin(95°).

Methods to Find Value of Sin 95 Degrees

The sine function is positive in the 2nd quadrant. The value of sin 95° is given as 0.99619. . .. We can find the value of sin 95 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 95° in Terms of Trigonometric Functions

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

• ± √(1-cos²(95°))
• ± tan 95°/√(1 + tan²(95°))
• ± 1/√(1 + cot²(95°))
• ± √(sec²(95°) - 1)/sec 95°
• 1/cosec 95°

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

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

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

Sin 95 Degrees Using Unit Circle

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

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

Hence the value of sin 95° = y = 0.9962 (approx)

☛ Also Check:

• sin 75 degrees
• sin 18 degrees
• sin 150 degrees
• sin 930 degrees
• sin 89 degrees
• sin 600 degrees

FAQs on Sin 95 Degrees

What is Sin 95 Degrees?

Sin 95 degrees is the value of sine trigonometric function for an angle equal to 95 degrees. The value of sin 95° is 0.9962 (approx).

How to Find the Value of Sin 95 Degrees?

The value of sin 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 sin 95° is equal to the y-coordinate (0.9962). ∴ sin 95° = 0.9962.

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

Since the cosecant function is the reciprocal of the sine function, we can write sin 95° as 1/cosec(95°). The value of cosec 95° is equal to 1.00381.

What is the Value of Sin 95 Degrees in Terms of Cot 95°?

We can represent the sine function in terms of the cotangent function using trig identities, sin 95° can be written as 1/√(1 + cot²(95°)). Here, the value of cot 95° is equal to -0.08748.

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

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

• ± √(1-cos²(95°))
• ± tan 95°/√(1 + tan²(95°))
• ± 1/√(1 + cot²(95°))
• ± √(sec²(95°) - 1)/sec 95°
• 1/cosec 95°

☛ Also check: trigonometric table