A day full of math games & activities. Find one near you.

Sin 7pi

The value of sin 7pi is 0. Sin 7pi radians in degrees is written as sin ((7π) × 180°/π), i.e., sin (1260°). In this article, we will discuss the methods to find the value of sin 7pi with examples.

Sin 7pi: 0
Sin (-7pi): 0
Sin 7pi in degrees: sin (1260°)

What is the Value of Sin 7pi?

The value of sin 7pi is 0. Sin 7pi can also be expressed using the equivalent of the given angle (7pi) in degrees (1260°).

We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 7pi radians = 7pi × (180°/pi) = 1260° or 1260 degrees
∴ sin 7pi = sin 7π = sin(1260°) = 0

Explanation:

For sin 7pi, the angle 7pi > 2pi. We can represent sin 7pi as, sin(7pi mod 2pi) = sin(pi). For sin 7pi, the angle 7pi lies on the negative x-axis. Thus, sin 7pi value = 0
Since the sine function is a periodic function, we can represent sin 7pi as, sin 7pi = sin(7pi + n × 2pi), n ∈ Z.
⇒ sin 7pi = sin 9pi = sin 11pi , and so on.
Note: Since, sine is an odd function, the value of sin(-7pi) = -sin(7pi) = 0.

Methods to Find Value of Sin 7pi

The value of sin 7pi is given as 0. We can find the value of sin 7pi by:

Using Unit Circle
Using Trigonometric Functions

Sin 7pi Using Unit Circle

To find the value of sin 7π using the unit circle, represent 7pi in the form (3 × 2pi) + pi [∵ 7pi>2pi] ∵ sine is a periodic function, sin 7pi = sin pi.

Rotate ‘r’ anticlockwise to form pi or 7pi angle with the positive x-axis.
The sin of 7pi equals the y-coordinate(0) of the point of intersection (-1, 0) of unit circle and r.

Hence the value of sin 7pi = y = 0

Sin 7pi in Terms of Trigonometric Functions

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

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

Note: Since 7pi lies on the negative x-axis, the final value of sin 7pi is 0.

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

sin(pi - 7pi) = sin(-6pi)
-sin(pi + 7pi) = -sin 8pi
cos(pi/2 - 7pi) = cos(-13pi/2)
-cos(pi/2 + 7pi) = -cos 15pi/2

☛ Also Check:

Examples Using Sin 7pi

Example 1: Simplify: 4 (sin(7pi)/sin(pi/2))

Solution:

We know sin 7pi = 0 and sin pi/2 = 1
⇒ 4 sin(7pi)/sin(pi/2) = 0
Example 2: Using the value of sin 7pi, solve: (1-cos²(7pi)).

Solution:
We know, (1-cos²(7pi)) = (sin²(7pi)) = 0
⇒ (1-cos²(7pi)) = 0
Example 3: Find the value of sin(7pi) if cos(7pi) is -1 and tan 7pi = 0.

Solution:
Since, tan 7pi = sin 7pi/cos 7pi
⇒ sin 7pi = 0

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on Sin 7pi

What is Sin 7pi?

Sin 7pi is the value of sine trigonometric function for an angle equal to 7pi radians. The value of sin 7pi is 0.

How to Find the Value of Sin 7pi?

The value of sin 7pi can be calculated by constructing an angle of 7π radians with the x-axis, and then finding the coordinates of the corresponding point (-1, 0) on the unit circle. The value of sin 7pi is equal to the y-coordinate (0). ∴ sin 7pi = 0.

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

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

What is the Value of Sin 7pi in Terms of Tan 7pi?

We know, using trig identities, we can write sin 7pi as -tan(7pi)/√(1 + tan²(7pi)). Here, the value of tan 7pi is equal to 0.

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

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

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

☛ Also check: trigonometric table

Download FREE Study Materials

Trigonometry

Math worksheets and
visual curriculum