Sin 35 Degrees
The value of sin 35 degrees is 0.5735764. . .. Sin 35 degrees in radians is written as sin (35° × π/180°), i.e., sin (7π/36) or sin (0.610865. . .). In this article, we will discuss the methods to find the value of sin 35 degrees with examples.
- Sin 35°: 0.5735764. . .
- Sin (-35 degrees): -0.5735764. . .
- Sin 35° in radians: sin (7π/36) or sin (0.6108652 . . .)
What is the Value of Sin 35 Degrees?
The value of sin 35 degrees in decimal is 0.573576436. . .. Sin 35 degrees can also be expressed using the equivalent of the given angle (35 degrees) in radians (0.61086 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 35 degrees = 35° × (π/180°) rad = 7π/36 or 0.6108 . . .
∴ sin 35° = sin(0.6108) = 0.5735764. . .
Explanation:
For sin 35 degrees, the angle 35° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 35° value = 0.5735764. . .
Since the sine function is a periodic function, we can represent sin 35° as, sin 35 degrees = sin(35° + n × 360°), n ∈ Z.
⇒ sin 35° = sin 395° = sin 755°, and so on.
Note: Since, sine is an odd function, the value of sin(-35°) = -sin(35°).
Methods to Find Value of Sin 35 Degrees
The sine function is positive in the 1st quadrant. The value of sin 35° is given as 0.57357. . .. We can find the value of sin 35 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Sin 35° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 35 degrees as:
- ± √(1-cos²(35°))
- ± tan 35°/√(1 + tan²(35°))
- ± 1/√(1 + cot²(35°))
- ± √(sec²(35°) - 1)/sec 35°
- 1/cosec 35°
Note: Since 35° lies in the 1st Quadrant, the final value of sin 35° will be positive.
We can use trigonometric identities to represent sin 35° as,
- sin(180° - 35°) = sin 145°
- -sin(180° + 35°) = -sin 215°
- cos(90° - 35°) = cos 55°
- -cos(90° + 35°) = -cos 125°
Sin 35 Degrees Using Unit Circle
To find the value of sin 35 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form a 35° angle with the positive x-axis.
- The sin of 35 degrees equals the y-coordinate(0.5736) of the point of intersection (0.8192, 0.5736) of unit circle and r.
Hence the value of sin 35° = y = 0.5736 (approx)
☛ Also Check:
FAQs on Sin 35 Degrees
What is Sin 35 Degrees?
Sin 35 degrees is the value of sine trigonometric function for an angle equal to 35 degrees. The value of sin 35° is 0.5736 (approx).
What is the Value of Sin 35 Degrees in Terms of Cos 35°?
Using trigonometric identities, we can write sin 35° in terms of cos 35° as, sin(35°) = √(1-cos²(35°)). Here, the value of cos 35° is equal to 0.8191520.
What is the Value of Sin 35° in Terms of Sec 35°?
Since the sine function can be represented using the secant function, we can write sin 35° as √(sec²(35°) - 1)/sec 35°. The value of sec 35° is equal to 1.220775.
How to Find the Value of Sin 35 Degrees?
The value of sin 35 degrees can be calculated by constructing an angle of 35° with the x-axis, and then finding the coordinates of the corresponding point (0.8192, 0.5736) on the unit circle. The value of sin 35° is equal to the y-coordinate (0.5736). ∴ sin 35° = 0.5736.
How to Find Sin 35° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 35° can be given in terms of other trigonometric functions as:
- ± √(1-cos²(35°))
- ± tan 35°/√(1 + tan²(35°))
- ± 1/√(1 + cot²(35°))
- ± √(sec²(35°) - 1)/sec 35°
- 1/cosec 35°
☛ Also check: trigonometric table