Exact Value Of Sin 105

Sin 105 Degrees

The value of sin 105 degrees is 0.9659258. . .. Sin 105 degrees in radians is written as sin (105° × π/180°), i.eastward., sin (7π/12) or sin (1.832595. . .). In this article, we will talk over the methods to find the value of sin 105 degrees with examples.

Sin 105°: 0.9659258. . .
Sin 105° in fraction: (√six + √2)/4
Sin (-105 degrees): -0.9659258. . .
Sin 105° in radians: sin (7π/12) or sin (i.8325957 . . .)

What is the Value of Sin 105 Degrees?

The value of sin 105 degrees in decimal is 0.965925826. . .. Sin 105 degrees can also be expressed using the equivalent of the given angle (105 degrees) in radians (1.83259 . . .).

Nosotros know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 105 degrees = 105° × (π/180°) rad = 7π/12 or 1.8325 . . .
∴ sin 105° = sin(1.8325) = (√half-dozen + √two)/4 or 0.9659258. . .

Sin 105 Degrees

Explanation:

For sin 105 degrees, the bending 105° lies between 90° and 180° (2d Quadrant). Since sine role is positive in the second quadrant, thus sin 105° value = (√6 + √2)/four or 0.9659258. . .
Since the sine part is a periodic function, nosotros tin represent sin 105° equally, sin 105 degrees = sin(105° + n × 360°), due north ∈ Z.
⇒ sin 105° = sin 465° = sin 825°, and and then on.
Notation: Since, sine is an odd role, the value of sin(-105°) = -sin(105°).

Methods to Find Value of Sin 105 Degrees

The sine part is positive in the 2nd quadrant. The value of sin 105° is given as 0.96592. . .. We tin notice the value of sin 105 degrees by:

Using Unit of measurement Circle
Using Trigonometric Functions

Sin 105 Degrees Using Unit Circle

value of sin 105

To find the value of sin 105 degrees using the unit of measurement circle:

Rotate 'r' anticlockwise to form a 105° angle with the positive x-axis.
The sin of 105 degrees equals the y-coordinate(0.9659) of the point of intersection (-0.2588, 0.9659) of unit circle and r.

Hence the value of sin 105° = y = 0.9659 (approx)

Sin 105° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 105 degrees equally:

± √(1-cos²(105°))
± tan 105°/√(1 + tan²(105°))
± 1/√(1 + cot²(105°))
± √(sec²(105°) - ane)/sec 105°
one/cosec 105°

Note: Since 105° lies in the 2nd Quadrant, the concluding value of sin 105° will be positive.

We tin utilize trigonometric identities to represent sin 105° equally,

sin(180° - 105°) = sin 75°
-sin(180° + 105°) = -sin 285°
cos(ninety° - 105°) = cos(-xv°)
-cos(xc° + 105°) = -cos 195°

☛ Also Check:

sin xc degrees
sin 104 degrees
sin sixty degrees
sin 12 degrees
sin 89 degrees
sin 356 degrees

FAQs on Sin 105 Degrees

What is Sin 105 Degrees?

Sin 105 degrees is the value of sine trigonometric function for an angle equal to 105 degrees. The value of sin 105° is (√6 + √2)/4 or 0.9659 (approx).

What is the Value of Sin 105 Degrees in Terms of Cot 105°?

We can represent the sine function in terms of the cotangent office using trig identities, sin 105° can exist written as 1/√(1 + cot²(105°)). Here, the value of cot 105° is equal to -0.26794.

How to Find Sin 105° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 105° can be given in terms of other trigonometric functions every bit:

± √(1-cos²(105°))
± tan 105°/√(ane + tan²(105°))
± 1/√(1 + cot²(105°))
± √(sec²(105°) - ane)/sec 105°
1/cosec 105°

☛ As well check: trigonometric table

How to Find the Value of Sin 105 Degrees?

The value of sin 105 degrees tin be calculated by amalgam an angle of 105° with the x-axis, and then finding the coordinates of the respective point (-0.2588, 0.9659) on the unit circle. The value of sin 105° is equal to the y-coordinate (0.9659). ∴ sin 105° = 0.9659.

What is the Exact Value of sin 105 Degrees?

The verbal value of sin 105 degrees tin can exist given accurately upwardly to 8 decimal places equally 0.96592582 and (√6 + √2)/4 in fraction.