Sin 42 Degrees

The value of sin 42 degrees is 0.6691306. . .. Sin 42 degrees in radians is written as sin (42° × π/180°), i.e., sin (7π/30) or sin (0.733038. . .). In this article, we will discuss the methods to find the value of sin 42 degrees with examples.

• Sin 42°: 0.6691306. . .
• Sin (-42 degrees): -0.6691306. . .
• Sin 42° in radians: sin (7π/30) or sin (0.7330382 . . .)

What is the Value of Sin 42 Degrees?

The value of sin 42 degrees in decimal is 0.669130606. . .. Sin 42 degrees can also be expressed using the equivalent of the given angle (42 degrees) in radians (0.73303 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 42 degrees = 42° × (π/180°) rad = 7π/30 or 0.7330 . . .
∴ sin 42° = sin(0.7330) = 0.6691306. . .

Explanation:

For sin 42 degrees, the angle 42° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 42° value = 0.6691306. . .
Since the sine function is a periodic function, we can represent sin 42° as, sin 42 degrees = sin(42° + n × 360°), n ∈ Z.
⇒ sin 42° = sin 402° = sin 762°, and so on.
Note: Since, sine is an odd function, the value of sin(-42°) = -sin(42°).

Methods to Find Value of Sin 42 Degrees

The sine function is positive in the 1st quadrant. The value of sin 42° is given as 0.66913. . .. We can find the value of sin 42 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 42 Degrees Using Unit Circle

To find the value of sin 42 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 42° angle with the positive x-axis.
• The sin of 42 degrees equals the y-coordinate(0.6691) of the point of intersection (0.7431, 0.6691) of unit circle and r.

Hence the value of sin 42° = y = 0.6691 (approx)

Sin 42° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 42 degrees as:

• ± √(1-cos²(42°))
• ± tan 42°/√(1 + tan²(42°))
• ± 1/√(1 + cot²(42°))
• ± √(sec²(42°) - 1)/sec 42°
• 1/cosec 42°

Note: Since 42° lies in the 1st Quadrant, the final value of sin 42° will be positive.

We can use trigonometric identities to represent sin 42° as,

• sin(180° - 42°) = sin 138°
• -sin(180° + 42°) = -sin 222°
• cos(90° - 42°) = cos 48°
• -cos(90° + 42°) = -cos 132°

☛ Also Check:

• sin 135 degrees
• sin 120 degrees
• sin 1 degrees
• sin 130 degrees
• sin 56 degrees
• sin 206 degrees

FAQs on Sin 42 Degrees

What is Sin 42 Degrees?

Sin 42 degrees is the value of sine trigonometric function for an angle equal to 42 degrees. The value of sin 42° is 0.6691 (approx).

What is the Value of Sin 42° in Terms of Cosec 42°?

Since the cosecant function is the reciprocal of the sine function, we can write sin 42° as 1/cosec(42°). The value of cosec 42° is equal to 1.49447.

How to Find the Value of Sin 42 Degrees?

The value of sin 42 degrees can be calculated by constructing an angle of 42° with the x-axis, and then finding the coordinates of the corresponding point (0.7431, 0.6691) on the unit circle. The value of sin 42° is equal to the y-coordinate (0.6691). ∴ sin 42° = 0.6691.

How to Find Sin 42° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 42° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(42°))
• ± tan 42°/√(1 + tan²(42°))
• ± 1/√(1 + cot²(42°))
• ± √(sec²(42°) - 1)/sec 42°
• 1/cosec 42°

☛ Also check: trigonometry table

What is the Value of Sin 42 Degrees in Terms of Cos 42°?

Using trigonometric identities, we can write sin 42° in terms of cos 42° as, sin(42°) = √(1-cos²(42°)). Here, the value of cos 42° is equal to 0.7431448.