Sin 88 Degrees

The value of sin 88 degrees is 0.9993908. . .. Sin 88 degrees in radians is written as sin (88° × π/180°), i.e., sin (22π/45) or sin (1.535889. . .). In this article, we will discuss the methods to find the value of sin 88 degrees with examples.

• Sin 88°: 0.9993908. . .
• Sin (-88 degrees): -0.9993908. . .
• Sin 88° in radians: sin (22π/45) or sin (1.5358897 . . .)

What is the Value of Sin 88 Degrees?

The value of sin 88 degrees in decimal is 0.999390827. . .. Sin 88 degrees can also be expressed using the equivalent of the given angle (88 degrees) in radians (1.53588 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 88 degrees = 88° × (π/180°) rad = 22π/45 or 1.5358 . . .
∴ sin 88° = sin(1.5358) = 0.9993908. . .

Explanation:

For sin 88 degrees, the angle 88° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 88° value = 0.9993908. . .
Since the sine function is a periodic function, we can represent sin 88° as, sin 88 degrees = sin(88° + n × 360°), n ∈ Z.
⇒ sin 88° = sin 448° = sin 808°, and so on.
Note: Since, sine is an odd function, the value of sin(-88°) = -sin(88°).

Methods to Find Value of Sin 88 Degrees

The sine function is positive in the 1st quadrant. The value of sin 88° is given as 0.99939. . .. We can find the value of sin 88 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 88° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 88 degrees as:

• ± √(1-cos²(88°))
• ± tan 88°/√(1 + tan²(88°))
• ± 1/√(1 + cot²(88°))
• ± √(sec²(88°) - 1)/sec 88°
• 1/cosec 88°

Note: Since 88° lies in the 1st Quadrant, the final value of sin 88° will be positive.

We can use trigonometric identities to represent sin 88° as,

• sin(180° - 88°) = sin 92°
• -sin(180° + 88°) = -sin 268°
• cos(90° - 88°) = cos 2°
• -cos(90° + 88°) = -cos 178°

Sin 88 Degrees Using Unit Circle

To find the value of sin 88 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 88° angle with the positive x-axis.
• The sin of 88 degrees equals the y-coordinate(0.9994) of the point of intersection (0.0349, 0.9994) of unit circle and r.

Hence the value of sin 88° = y = 0.9994 (approx)

☛ Also Check:

• sin 13 degrees
• sin 75 degrees
• sin 45 degrees
• sin 260 degrees
• sin 585 degrees
• sin 51 degrees

FAQs on Sin 88 Degrees

What is Sin 88 Degrees?

Sin 88 degrees is the value of sine trigonometric function for an angle equal to 88 degrees. The value of sin 88° is 0.9994 (approx).

What is the Value of Sin 88° in Terms of Sec 88°?

Since the sine function can be represented using the secant function, we can write sin 88° as √(sec²(88°) - 1)/sec 88°. The value of sec 88° is equal to 28.653708.

How to Find Sin 88° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 88° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(88°))
• ± tan 88°/√(1 + tan²(88°))
• ± 1/√(1 + cot²(88°))
• ± √(sec²(88°) - 1)/sec 88°
• 1/cosec 88°

☛ Also check: trigonometry table

How to Find the Value of Sin 88 Degrees?

The value of sin 88 degrees can be calculated by constructing an angle of 88° with the x-axis, and then finding the coordinates of the corresponding point (0.0349, 0.9994) on the unit circle. The value of sin 88° is equal to the y-coordinate (0.9994). ∴ sin 88° = 0.9994.

What is the Value of Sin 88 Degrees in Terms of Cot 88°?

We can represent the sine function in terms of the cotangent function using trig identities, sin 88° can be written as 1/√(1 + cot²(88°)). Here, the value of cot 88° is equal to 0.03492.