Sin 195 Degrees
The value of sin 195 degrees is -0.2588190. . .. Sin 195 degrees in radians is written as sin (195° × π/180°), i.e., sin (13π/12) or sin (3.403392. . .). In this article, we will discuss the methods to find the value of sin 195 degrees with examples.
- Sin 195°: -0.2588190. . .
- Sin 195° in fraction: -(√6 - √2)/4
- Sin (-195 degrees): 0.2588190. . .
- Sin 195° in radians: sin (13π/12) or sin (3.4033920 . . .)
What is the Value of Sin 195 Degrees?
The value of sin 195 degrees in decimal is -0.258819045. . .. Sin 195 degrees can also be expressed using the equivalent of the given angle (195 degrees) in radians (3.40339 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 195 degrees = 195° × (π/180°) rad = 13π/12 or 3.4033 . . .
∴ sin 195° = sin(3.4033) = -(√6 - √2)/4 or -0.2588190. . .
Explanation:
For sin 195 degrees, the angle 195° lies between 180° and 270° (Third Quadrant). Since sine function is negative in the third quadrant, thus sin 195° value = -(√6 - √2)/4 or -0.2588190. . .
Since the sine function is a periodic function, we can represent sin 195° as, sin 195 degrees = sin(195° + n × 360°), n ∈ Z.
⇒ sin 195° = sin 555° = sin 915°, and so on.
Note: Since, sine is an odd function, the value of sin(-195°) = -sin(195°).
Methods to Find Value of Sin 195 Degrees
The sine function is negative in the 3rd quadrant. The value of sin 195° is given as -0.25881. . .. We can find the value of sin 195 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Sin 195 Degrees Using Unit Circle
To find the value of sin 195 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form a 195° angle with the positive x-axis.
- The sin of 195 degrees equals the y-coordinate(-0.2588) of the point of intersection (-0.9659, -0.2588) of unit circle and r.
Hence the value of sin 195° = y = -0.2588 (approx)
Sin 195° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 195 degrees as:
- ± √(1-cos²(195°))
- ± tan 195°/√(1 + tan²(195°))
- ± 1/√(1 + cot²(195°))
- ± √(sec²(195°) - 1)/sec 195°
- 1/cosec 195°
Note: Since 195° lies in the 3rd Quadrant, the final value of sin 195° will be negative.
We can use trigonometric identities to represent sin 195° as,
- sin(180° - 195°) = sin(-15°)
- -sin(180° + 195°) = -sin 375°
- cos(90° - 195°) = cos(-105°)
- -cos(90° + 195°) = -cos 285°
☛ Also Check:
FAQs on Sin 195 Degrees
What is Sin 195 Degrees?
Sin 195 degrees is the value of sine trigonometric function for an angle equal to 195 degrees. The value of sin 195° is -(√6 - √2)/4 or -0.2588 (approx).
What is the Value of Sin 195 Degrees in Terms of Cos 195°?
Using trigonometric identities, we can write sin 195° in terms of cos 195° as, sin(195°) = -√(1-cos²(195°)). Here, the value of cos 195° is equal to -(√6+√2)/4.
How to Find Sin 195° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 195° can be given in terms of other trigonometric functions as:
- ± √(1-cos²(195°))
- ± tan 195°/√(1 + tan²(195°))
- ± 1/√(1 + cot²(195°))
- ± √(sec²(195°) - 1)/sec 195°
- 1/cosec 195°
☛ Also check: trigonometry table
What is the Value of Sin 195° in Terms of Sec 195°?
Since the sine function can be represented using the secant function, we can write sin 195° as √(sec²(195°) - 1)/sec 195°. The value of sec 195° is equal to -1.035276.
How to Find the Value of Sin 195 Degrees?
The value of sin 195 degrees can be calculated by constructing an angle of 195° with the x-axis, and then finding the coordinates of the corresponding point (-0.9659, -0.2588) on the unit circle. The value of sin 195° is equal to the y-coordinate (-0.2588). ∴ sin 195° = -0.2588.