Sin 158 Degrees

The value of sin 158 degrees is 0.3746065. . .. Sin 158 degrees in radians is written as sin (158° × π/180°), i.e., sin (79π/90) or sin (2.757620. . .). In this article, we will discuss the methods to find the value of sin 158 degrees with examples.

• Sin 158°: 0.3746065. . .
• Sin (-158 degrees): -0.3746065. . .
• Sin 158° in radians: sin (79π/90) or sin (2.7576202 . . .)

What is the Value of Sin 158 Degrees?

The value of sin 158 degrees in decimal is 0.374606593. . .. Sin 158 degrees can also be expressed using the equivalent of the given angle (158 degrees) in radians (2.75762 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 158 degrees = 158° × (π/180°) rad = 79π/90 or 2.7576 . . .
∴ sin 158° = sin(2.7576) = 0.3746065. . .

Explanation:

For sin 158 degrees, the angle 158° lies between 90° and 180° (Second Quadrant). Since sine function is positive in the second quadrant, thus sin 158° value = 0.3746065. . .
Since the sine function is a periodic function, we can represent sin 158° as, sin 158 degrees = sin(158° + n × 360°), n ∈ Z.
⇒ sin 158° = sin 518° = sin 878°, and so on.
Note: Since, sine is an odd function, the value of sin(-158°) = -sin(158°).

Methods to Find Value of Sin 158 Degrees

The sine function is positive in the 2nd quadrant. The value of sin 158° is given as 0.37460. . .. We can find the value of sin 158 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 158° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 158 degrees as:

• ± √(1-cos²(158°))
• ± tan 158°/√(1 + tan²(158°))
• ± 1/√(1 + cot²(158°))
• ± √(sec²(158°) - 1)/sec 158°
• 1/cosec 158°

Note: Since 158° lies in the 2nd Quadrant, the final value of sin 158° will be positive.

We can use trigonometric identities to represent sin 158° as,

• sin(180° - 158°) = sin 22°
• -sin(180° + 158°) = -sin 338°
• cos(90° - 158°) = cos(-68°)
• -cos(90° + 158°) = -cos 248°

Sin 158 Degrees Using Unit Circle

To find the value of sin 158 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 158° angle with the positive x-axis.
• The sin of 158 degrees equals the y-coordinate(0.3746) of the point of intersection (-0.9272, 0.3746) of unit circle and r.

Hence the value of sin 158° = y = 0.3746 (approx)

☛ Also Check:

• sin 3 degrees
• sin 2 degrees
• sin 11 degrees
• sin 960 degrees
• sin 495 degrees
• sin 356 degrees

FAQs on Sin 158 Degrees

What is Sin 158 Degrees?

Sin 158 degrees is the value of sine trigonometric function for an angle equal to 158 degrees. The value of sin 158° is 0.3746 (approx).

What is the Exact Value of sin 158 Degrees?

The exact value of sin 158 degrees can be given accurately up to 8 decimal places as 0.37460659.

How to Find the Value of Sin 158 Degrees?

The value of sin 158 degrees can be calculated by constructing an angle of 158° with the x-axis, and then finding the coordinates of the corresponding point (-0.9272, 0.3746) on the unit circle. The value of sin 158° is equal to the y-coordinate (0.3746). ∴ sin 158° = 0.3746.

What is the Value of Sin 158 Degrees in Terms of Cos 158°?

Using trigonometric identities, we can write sin 158° in terms of cos 158° as, sin(158°) = √(1-cos²(158°)). Here, the value of cos 158° is equal to -0.9271838.

How to Find Sin 158° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 158° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(158°))
• ± tan 158°/√(1 + tan²(158°))
• ± 1/√(1 + cot²(158°))
• ± √(sec²(158°) - 1)/sec 158°
• 1/cosec 158°

☛ Also check: trigonometry table