Sin 68 Degrees

The value of sin 68 degrees is 0.9271838. . .. Sin 68 degrees in radians is written as sin (68° × π/180°), i.e., sin (17π/45) or sin (1.186823. . .). In this article, we will discuss the methods to find the value of sin 68 degrees with examples.

• Sin 68°: 0.9271838. . .
• Sin (-68 degrees): -0.9271838. . .
• Sin 68° in radians: sin (17π/45) or sin (1.1868238 . . .)

What is the Value of Sin 68 Degrees?

The value of sin 68 degrees in decimal is 0.927183854. . .. Sin 68 degrees can also be expressed using the equivalent of the given angle (68 degrees) in radians (1.18682 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 68 degrees = 68° × (π/180°) rad = 17π/45 or 1.1868 . . .
∴ sin 68° = sin(1.1868) = 0.9271838. . .

Explanation:

For sin 68 degrees, the angle 68° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 68° value = 0.9271838. . .
Since the sine function is a periodic function, we can represent sin 68° as, sin 68 degrees = sin(68° + n × 360°), n ∈ Z.
⇒ sin 68° = sin 428° = sin 788°, and so on.
Note: Since, sine is an odd function, the value of sin(-68°) = -sin(68°).

Methods to Find Value of Sin 68 Degrees

The sine function is positive in the 1st quadrant. The value of sin 68° is given as 0.92718. . .. We can find the value of sin 68 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 68° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 68 degrees as:

• ± √(1-cos²(68°))
• ± tan 68°/√(1 + tan²(68°))
• ± 1/√(1 + cot²(68°))
• ± √(sec²(68°) - 1)/sec 68°
• 1/cosec 68°

Note: Since 68° lies in the 1st Quadrant, the final value of sin 68° will be positive.

We can use trigonometric identities to represent sin 68° as,

• sin(180° - 68°) = sin 112°
• -sin(180° + 68°) = -sin 248°
• cos(90° - 68°) = cos 22°
• -cos(90° + 68°) = -cos 158°

Sin 68 Degrees Using Unit Circle

To find the value of sin 68 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 68° angle with the positive x-axis.
• The sin of 68 degrees equals the y-coordinate(0.9272) of the point of intersection (0.3746, 0.9272) of unit circle and r.

Hence the value of sin 68° = y = 0.9272 (approx)

☛ Also Check:

• sin 45 degrees
• sin 50 degrees
• sin 1 degrees
• sin 600 degrees
• sin 6 degrees
• sin 240 degrees

FAQs on Sin 68 Degrees

What is Sin 68 Degrees?

Sin 68 degrees is the value of sine trigonometric function for an angle equal to 68 degrees. The value of sin 68° is 0.9272 (approx).

How to Find the Value of Sin 68 Degrees?

The value of sin 68 degrees can be calculated by constructing an angle of 68° with the x-axis, and then finding the coordinates of the corresponding point (0.3746, 0.9272) on the unit circle. The value of sin 68° is equal to the y-coordinate (0.9272). ∴ sin 68° = 0.9272.

What is the Exact Value of sin 68 Degrees?

The exact value of sin 68 degrees can be given accurately up to 8 decimal places as 0.92718385.

What is the Value of Sin 68 Degrees in Terms of Cos 68°?

Using trigonometric identities, we can write sin 68° in terms of cos 68° as, sin(68°) = √(1-cos²(68°)). Here, the value of cos 68° is equal to 0.3746065.

How to Find Sin 68° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 68° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(68°))
• ± tan 68°/√(1 + tan²(68°))
• ± 1/√(1 + cot²(68°))
• ± √(sec²(68°) - 1)/sec 68°
• 1/cosec 68°

☛ Also check: trigonometric table