# Sin 195

Sin 195.

## 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:
-(√half-dozen – √2)/4
• Sin (-195 degrees):
0.2588190. . .

sin (13π/12) or sin (iii.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 (three.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) = -(√vi – √two)/four or -0.2588190. . .

Caption:

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)/four 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°).

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## Methods to Find Value of Sin 195 Degrees

The sine role is negative in the third quadrant. The value of sin 195° is given as -0.25881. . .. Nosotros tin can observe the value of sin 195 degrees by:

• Using Unit of measurement Circle
• Using Trigonometric Functions

## Sin 195 Degrees Using Unit Circumvolve

To detect the value of sin 195 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 195° bending with the positive x-centrality.
• The sin of 195 degrees equals the y-coordinate(-0.2588) of the point of intersection (-0.9659, -0.2588) of unit of measurement 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°))
• ± i/√(1 + cot²(195°))
• ± √(sec²(195°) – 1)/sec 195°
• i/cosec 195°

Note: Since 195° lies in the 3rd Quadrant, the final value of sin 195° will exist negative.

We can use trigonometric identities to represent sin 195° as,

• sin(180° – 195°) = sin(-15°)
• -sin(180° + 195°) = -sin 375°
• cos(xc° – 195°) = cos(-105°)
• -cos(ninety° + 195°) = -cos 285°

☛ Also Check:

• sin 45 degrees
• sin 150 degrees
• sin 2 degrees
• sin 7 degrees
• sin 21 degrees
• sin 140 degrees

## 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 -(√six – √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)/four.

### 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°/√(one + tan²(195°))
• ± one/√(1 + cot²(195°))
• ± √(sec²(195°) – 1)/sec 195°
• 1/cosec 195°

☛ Also bank 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 tin write sin 195° as √(sec²(195°) – 1)/sec 195°. The value of sec 195° is equal to -ane.035276.

### How to Notice 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 bespeak (-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.

## Sin 195

Source: https://www.cuemath.com/trigonometry/sin-195-degrees/

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