Sin 7 Degrees

The value of sin 7 degrees is 0.1218693. . .. Sin 7 degrees in radians is written as sin (7° × π/180°), i.e., sin (0.122173. . .). In this article, we will discuss the methods to find the value of sin 7 degrees with examples.

• Sin 7°: 0.1218693. . .
• Sin (-7 degrees): -0.1218693. . .
• Sin 7° in radians: sin (0.1221730 . . .)

What is the Value of Sin 7 Degrees?

The value of sin 7 degrees in decimal is 0.121869343. . .. Sin 7 degrees can also be expressed using the equivalent of the given angle (7 degrees) in radians (0.12217 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 7 degrees = 7° × (π/180°) rad = 0.1221 . . .
∴ sin 7° = sin(0.1221) = 0.1218693. . .

Explanation:

For sin 7 degrees, the angle 7° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 7° value = 0.1218693. . .
Since the sine function is a periodic function, we can represent sin 7° as, sin 7 degrees = sin(7° + n × 360°), n ∈ Z.
⇒ sin 7° = sin 367° = sin 727°, and so on.
Note: Since, sine is an odd function, the value of sin(-7°) = -sin(7°).

Methods to Find Value of Sin 7 Degrees

The sine function is positive in the 1st quadrant. The value of sin 7° is given as 0.12186. . .. We can find the value of sin 7 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 7° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 7 degrees as:

• ± √(1-cos²(7°))
• ± tan 7°/√(1 + tan²(7°))
• ± 1/√(1 + cot²(7°))
• ± √(sec²(7°) - 1)/sec 7°
• 1/cosec 7°

Note: Since 7° lies in the 1st Quadrant, the final value of sin 7° will be positive.

We can use trigonometric identities to represent sin 7° as,

• sin(180° - 7°) = sin 173°
• -sin(180° + 7°) = -sin 187°
• cos(90° - 7°) = cos 83°
• -cos(90° + 7°) = -cos 97°

Sin 7 Degrees Using Unit Circle

To find the value of sin 7 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 7° angle with the positive x-axis.
• The sin of 7 degrees equals the y-coordinate(0.1219) of the point of intersection (0.9925, 0.1219) of unit circle and r.

Hence the value of sin 7° = y = 0.1219 (approx)

☛ Also Check:

• sin 18 degrees
• sin 2 degrees
• sin 45 degrees
• sin 44 degrees
• sin 108 degrees
• sin 96 degrees

FAQs on Sin 7 Degrees

What is Sin 7 Degrees?

Sin 7 degrees is the value of sine trigonometric function for an angle equal to 7 degrees. The value of sin 7° is 0.1219 (approx).

How to Find Sin 7° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 7° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(7°))
• ± tan 7°/√(1 + tan²(7°))
• ± 1/√(1 + cot²(7°))
• ± √(sec²(7°) - 1)/sec 7°
• 1/cosec 7°

☛ Also check: trigonometric table

How to Find the Value of Sin 7 Degrees?

The value of sin 7 degrees can be calculated by constructing an angle of 7° with the x-axis, and then finding the coordinates of the corresponding point (0.9925, 0.1219) on the unit circle. The value of sin 7° is equal to the y-coordinate (0.1219). ∴ sin 7° = 0.1219.

What is the Value of Sin 7° in Terms of Sec 7°?

Since the sine function can be represented using the secant function, we can write sin 7° as √(sec²(7°) - 1)/sec 7°. The value of sec 7° is equal to 1.00751.

What is the Value of Sin 7 Degrees in Terms of Tan 7°?

We know, using trig identities, we can write sin 7° as tan 7°/√(1 + tan²(7°)). Here, the value of tan 7° is equal to 0.122784.