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.e., sin (7π/12) or sin (1.832595. . .). In this article, we will discuss the methods to find the value of sin 105 degrees with examples.

• Sin 105°: 0.9659258. . .
• Sin 105° in fraction: (√6 + √2)/4
• Sin (-105 degrees): -0.9659258. . .
• Sin 105° in radians: sin (7π/12) or sin (1.8325957 . . .)

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 . . .).

We 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) = (√6 + √2)/4 or 0.9659258. . .

Explanation:

For sin 105 degrees, the angle 105° lies between 90° and 180° (Second Quadrant). Since sine function is positive in the second quadrant, thus sin 105° value = (√6 + √2)/4 or 0.9659258. . .
Since the sine function is a periodic function, we can represent sin 105° as, sin 105 degrees = sin(105° + n × 360°), n ∈ Z.
⇒ sin 105° = sin 465° = sin 825°, and so on.
Note: Since, sine is an odd function, the value of sin(-105°) = -sin(105°).

Methods to Find Value of Sin 105 Degrees

The sine function is positive in the 2nd quadrant. The value of sin 105° is given as 0.96592. . .. We can find the value of sin 105 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 105 Degrees Using Unit Circle

To find the value of sin 105 degrees using the unit 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 as:

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

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

We can use trigonometric identities to represent sin 105° as,

• sin(180° - 105°) = sin 75°
• -sin(180° + 105°) = -sin 285°
• cos(90° - 105°) = cos(-15°)
• -cos(90° + 105°) = -cos 195°

☛ Also Check:

• sin 90 degrees
• sin 104 degrees
• sin 60 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 function using trig identities, sin 105° can be 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 as:

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

☛ Also check: trigonometric table

How to Find the Value of Sin 105 Degrees?

The value of sin 105 degrees can be calculated by constructing an angle of 105° with the x-axis, and then finding the coordinates of the corresponding 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 exact value of sin 105 degrees can be given accurately up to 8 decimal places as 0.96592582 and (√6 + √2)/4 in fraction.