Sin 7pi/2

The value of sin 7pi/2 is -1. Sin 7pi/2 radians in degrees is written as sin ((7π/2) × 180°/π), i.e., sin (630°). In this article, we will discuss the methods to find the value of sin 7pi/2 with examples.

• Sin 7pi/2: -1
• Sin (-7pi/2): 1
• Sin 7pi/2 in degrees: sin (630°)

What is the Value of Sin 7pi/2?

The value of sin 7pi/2 is -1. Sin 7pi/2 can also be expressed using the equivalent of the given angle (7pi/2) in degrees (630°).

We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 7pi/2 radians = 7pi/2 × (180°/pi) = 630° or 630 degrees
∴ sin 7pi/2 = sin 7π/2 = sin(630°) = -1

Explanation:

For sin 7pi/2, the angle 7pi/2 > 2pi. We can represent sin 7pi/2 as, sin(7pi/2 mod 2pi) = sin(3pi/2). For sin 7pi/2, the angle 7pi/2 lies on the negative y-axis. Thus, sin 7pi/2 value = -1
Since the sine function is a periodic function, we can represent sin 7pi/2 as, sin 7pi/2 = sin(7pi/2 + n × 2pi), n ∈ Z.
⇒ sin 7pi/2 = sin 11pi/2 = sin 15pi/2 , and so on.
Note: Since, sine is an odd function, the value of sin(-7pi/2) = -sin(7pi/2).

Methods to Find Value of Sin 7pi/2

The value of sin 7pi/2 is given as -1. We can find the value of sin 7pi/2 by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 7pi/2 Using Unit Circle

To find the value of sin 7π/2 using the unit circle, represent 7pi/2 in the form (1 × 2pi) + 3pi/2 [∵ 7pi/2>2pi] ∵ sine is a periodic function, sin 7pi/2 = sin 3pi/2.

• Rotate ‘r’ anticlockwise to form 3pi/2 or 7pi/2 angle with the positive x-axis.
• The sin of 7pi/2 equals the y-coordinate(-1) of the point of intersection (0, -1) of unit circle and r.

Hence the value of sin 7pi/2 = y = -1

Sin 7pi/2 in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 7pi/2 as:

• ± √(1-cos²(7pi/2))
• ± tan(7pi/2)/√(1 + tan²(7pi/2))
• ± 1/√(1 + cot²(7pi/2))
• ± √(sec²(7pi/2) - 1)/sec(7pi/2)
• 1/cosec(7pi/2)

Note: Since 7pi/2 lies on the negative y-axis, the final value of sin 7pi/2 is -1.

We can use trigonometric identities to represent sin 7pi/2 as,

• sin(pi - 7pi/2) = sin(-5pi/2)
• -sin(pi + 7pi/2) = -sin 9pi/2
• cos(pi/2 - 7pi/2) = cos(-3pi)
• -cos(pi/2 + 7pi/2) = -cos 4pi

☛ Also Check:

• sin 5pi/8
• sin 3pi/2
• tan 7pi/8
• tan 5pi/12
• tan pi/8
• tan 2pi

FAQs on Sin 7pi/2

What is Sin 7pi/2?

Sin 7pi/2 is the value of sine trigonometric function for an angle equal to 7pi/2 radians. The value of sin 7pi/2 is -1.

What is the Value of Sin 7pi/2 in Terms of Sec 7pi/2?

Since the sine function can be represented using the secant function, we can write sin 7pi/2 as √(sec²(7pi/2) - 1)/sec 7pi/2.

How to Find the Value of Sin 7pi/2?

The value of sin 7pi/2 can be calculated by constructing an angle of 7π/2 radians with the x-axis, and then finding the coordinates of the corresponding point (0, -1) on the unit circle. The value of sin 7pi/2 is equal to the y-coordinate (-1). ∴ sin 7pi/2 = -1.

What is the Value of Sin 7pi/2 in Terms of Cot 7pi/2?

We can represent the sine function in terms of the cotangent function using trig identities, sin 7pi/2 can be written as -1/√(1 + cot²(7pi/2)). Here, the value of cot 7pi/2 is equal to 0.

How to Find Sin 7pi/2 in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 7π/2 can be given in terms of other trigonometric functions as:

• ± √(1-cos²(7pi/2))
• ± tan(7pi/2)/√(1 + tan²(7pi/2))
• ± 1/√(1 + cot²(7pi/2))
• ± √(sec²(7pi/2) - 1)/sec(7pi/2)
• 1/cosec(7pi/2)

☛ Also check: trigonometry table