Sin 46 Degrees
The value of sin 46 degrees is 0.7193398. . .. Sin 46 degrees in radians is written as sin (46° × π/180°), i.e., sin (23π/90) or sin (0.802851. . .). In this article, we will discuss the methods to find the value of sin 46 degrees with examples.
 Sin 46°: 0.7193398. . .
 Sin (46 degrees): 0.7193398. . .
 Sin 46° in radians: sin (23π/90) or sin (0.8028514 . . .)
What is the Value of Sin 46 Degrees?
The value of sin 46 degrees in decimal is 0.719339800. . .. Sin 46 degrees can also be expressed using the equivalent of the given angle (46 degrees) in radians (0.80285 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 46 degrees = 46° × (π/180°) rad = 23π/90 or 0.8028 . . .
∴ sin 46° = sin(0.8028) = 0.7193398. . .
Explanation:
For sin 46 degrees, the angle 46° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 46° value = 0.7193398. . .
Since the sine function is a periodic function, we can represent sin 46° as, sin 46 degrees = sin(46° + n × 360°), n ∈ Z.
⇒ sin 46° = sin 406° = sin 766°, and so on.
Note: Since, sine is an odd function, the value of sin(46°) = sin(46°).
Methods to Find Value of Sin 46 Degrees
The sine function is positive in the 1st quadrant. The value of sin 46° is given as 0.71933. . .. We can find the value of sin 46 degrees by:
 Using Trigonometric Functions
 Using Unit Circle
Sin 46° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 46 degrees as:
 ± √(1cos²(46°))
 ± tan 46°/√(1 + tan²(46°))
 ± 1/√(1 + cot²(46°))
 ± √(sec²(46°)  1)/sec 46°
 1/cosec 46°
Note: Since 46° lies in the 1st Quadrant, the final value of sin 46° will be positive.
We can use trigonometric identities to represent sin 46° as,
 sin(180°  46°) = sin 134°
 sin(180° + 46°) = sin 226°
 cos(90°  46°) = cos 44°
 cos(90° + 46°) = cos 136°
Sin 46 Degrees Using Unit Circle
To find the value of sin 46 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form a 46° angle with the positive xaxis.
 The sin of 46 degrees equals the ycoordinate(0.7193) of the point of intersection (0.6947, 0.7193) of unit circle and r.
Hence the value of sin 46° = y = 0.7193 (approx)
☛ Also Check:
Examples Using Sin 46 Degrees

Example 1: Find the value of sin 46° if cosec 46° is 1.3901.
Solution:
Since, sin 46° = 1/csc 46°
⇒ sin 46° = 1/1.3901 = 0.7193 
Example 2: Find the value of 5 sin(46°)/7 cos(44°).
Solution:
Using trigonometric identities, we know, sin(46°) = cos(90°  46°) = cos 44°.
⇒ sin(46°) = cos(44°)
⇒ Value of 5 sin(46°)/7 cos(44°) = 5/7 
Example 3: Using the value of sin 46°, solve: (1cos²(46°)).
Solution:
We know, (1cos²(46°)) = (sin²(46°)) = 0.5174
⇒ (1cos²(46°)) = 0.5174
FAQs on Sin 46 Degrees
What is Sin 46 Degrees?
Sin 46 degrees is the value of sine trigonometric function for an angle equal to 46 degrees. The value of sin 46° is 0.7193 (approx).
What is the Value of Sin 46 Degrees in Terms of Cos 46°?
Using trigonometric identities, we can write sin 46° in terms of cos 46° as, sin(46°) = √(1cos²(46°)). Here, the value of cos 46° is equal to 0.6946583.
How to Find the Value of Sin 46 Degrees?
The value of sin 46 degrees can be calculated by constructing an angle of 46° with the xaxis, and then finding the coordinates of the corresponding point (0.6947, 0.7193) on the unit circle. The value of sin 46° is equal to the ycoordinate (0.7193). ∴ sin 46° = 0.7193.
How to Find Sin 46° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 46° can be given in terms of other trigonometric functions as:
 ± √(1cos²(46°))
 ± tan 46°/√(1 + tan²(46°))
 ± 1/√(1 + cot²(46°))
 ± √(sec²(46°)  1)/sec 46°
 1/cosec 46°
☛ Also check: trigonometry table
What is the Value of Sin 46° in Terms of Cosec 46°?
Since the cosecant function is the reciprocal of the sine function, we can write sin 46° as 1/cosec(46°). The value of cosec 46° is equal to 1.39016.
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