Sin 78 Degrees
The value of sin 78 degrees is 0.9781476. . .. Sin 78 degrees in radians is written as sin (78° × π/180°), i.e., sin (13π/30) or sin (1.361356. . .). In this article, we will discuss the methods to find the value of sin 78 degrees with examples.
 Sin 78°: 0.9781476. . .
 Sin (78 degrees): 0.9781476. . .
 Sin 78° in radians: sin (13π/30) or sin (1.3613568 . . .)
What is the Value of Sin 78 Degrees?
The value of sin 78 degrees in decimal is 0.978147600. . .. Sin 78 degrees can also be expressed using the equivalent of the given angle (78 degrees) in radians (1.36135 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 78 degrees = 78° × (π/180°) rad = 13π/30 or 1.3613 . . .
∴ sin 78° = sin(1.3613) = 0.9781476. . .
Explanation:
For sin 78 degrees, the angle 78° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 78° value = 0.9781476. . .
Since the sine function is a periodic function, we can represent sin 78° as, sin 78 degrees = sin(78° + n × 360°), n ∈ Z.
⇒ sin 78° = sin 438° = sin 798°, and so on.
Note: Since, sine is an odd function, the value of sin(78°) = sin(78°).
Methods to Find Value of Sin 78 Degrees
The sine function is positive in the 1st quadrant. The value of sin 78° is given as 0.97814. . .. We can find the value of sin 78 degrees by:
 Using Trigonometric Functions
 Using Unit Circle
Sin 78° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 78 degrees as:
 ± √(1cos²(78°))
 ± tan 78°/√(1 + tan²(78°))
 ± 1/√(1 + cot²(78°))
 ± √(sec²(78°)  1)/sec 78°
 1/cosec 78°
Note: Since 78° lies in the 1st Quadrant, the final value of sin 78° will be positive.
We can use trigonometric identities to represent sin 78° as,
 sin(180°  78°) = sin 102°
 sin(180° + 78°) = sin 258°
 cos(90°  78°) = cos 12°
 cos(90° + 78°) = cos 168°
Sin 78 Degrees Using Unit Circle
To find the value of sin 78 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form a 78° angle with the positive xaxis.
 The sin of 78 degrees equals the ycoordinate(0.9781) of the point of intersection (0.2079, 0.9781) of unit circle and r.
Hence the value of sin 78° = y = 0.9781 (approx)
☛ Also Check:
Examples Using Sin 78 Degrees

Example 1: Find the value of sin 78° if cosec 78° is 1.0223.
Solution:
Since, sin 78° = 1/csc 78°
⇒ sin 78° = 1/1.0223 = 0.9781 
Example 2: Find the value of 5 sin(78°)/7 cos(12°).
Solution:
Using trigonometric identities, we know, sin(78°) = cos(90°  78°) = cos 12°.
⇒ sin(78°) = cos(12°)
⇒ Value of 5 sin(78°)/7 cos(12°) = 5/7 
Example 3: Using the value of sin 78°, solve: (1cos²(78°)).
Solution:
We know, (1cos²(78°)) = (sin²(78°)) = 0.9568
⇒ (1cos²(78°)) = 0.9568
FAQs on Sin 78 Degrees
What is Sin 78 Degrees?
Sin 78 degrees is the value of sine trigonometric function for an angle equal to 78 degrees. The value of sin 78° is 0.9781 (approx).
What is the Value of Sin 78 Degrees in Terms of Tan 78°?
We know, using trig identities, we can write sin 78° as tan 78°/√(1 + tan²(78°)). Here, the value of tan 78° is equal to 4.704630.
What is the Value of Sin 78° in Terms of Sec 78°?
Since the sine function can be represented using the secant function, we can write sin 78° as √(sec²(78°)  1)/sec 78°. The value of sec 78° is equal to 4.809734.
How to Find Sin 78° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 78° can be given in terms of other trigonometric functions as:
 ± √(1cos²(78°))
 ± tan 78°/√(1 + tan²(78°))
 ± 1/√(1 + cot²(78°))
 ± √(sec²(78°)  1)/sec 78°
 1/cosec 78°
☛ Also check: trigonometry table
How to Find the Value of Sin 78 Degrees?
The value of sin 78 degrees can be calculated by constructing an angle of 78° with the xaxis, and then finding the coordinates of the corresponding point (0.2079, 0.9781) on the unit circle. The value of sin 78° is equal to the ycoordinate (0.9781). ∴ sin 78° = 0.9781.
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