Which of the following is the value of sin((pi)/(2)) ? Choose 1 answer: (A) -1 (B) 0 (C) (sqrt2)/(2) (D) 1

Introduction to sine function: We know that the sine function is one of the basic trigonometric functions. The value of sin(θ) depends on the angle θ. We need to find the value of sin((pi)/(2)), which is the sine of 90 degrees.Conversion of radians to degrees: The angle (pi)/(2) radians is equivalent to 90 degrees. The sine of 90 degrees is a well-known value in the unit circle, where the sine of an angle is the y-coordinate of the corresponding point on the unit circle.Finding the point on the unit circle: At 90 degrees or (pi)/(2) radians, the point on the unit circle is (0, 1). Therefore, the y-coordinate, which gives us the sine value, is 1.Determining the sine value: Since the y-coordinate is 1, the value of sin((pi)/(2)) is 1. This corresponds to choice (D) in the given options.

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Which of the following is the value of
sin((pi)/(2)) ?
Choose 1 answer:
(A) -1
(B) 0
(C)
(sqrt2)/(2)
(D) 1

Which of the following is the value of $\sin \left(\frac{\pi}{2}\right) ?$ $\newline$ Choose $1$ answer: $\newline$ (A) $-1$ $\newline$ (B) $0$ $\newline$ (C) $\frac{\sqrt{2}}{2}$ $\newline$ (D) $1$

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Math Problems

Grade 8

Mean, median, mode, and range: find the missing number

Full solution

Q. Which of the following is the value of

\sin \left(\frac{\pi}{2}\right) ?

\newline

Choose

1

answer:

\newline

(A)

-1

\newline

(B)

0

\newline

(C)

\frac{\sqrt{2}}{2}

\newline

(D)

1

Introduction to sine function: We know that the sine function is one of the basic trigonometric functions. The value of $\sin(\theta)$ depends on the angle $\theta$ . We need to find the value of $\sin\left(\frac{\pi}{2}\right)$ , which is the sine of $90$ degrees.
Conversion of radians to degrees: The angle $\frac{\pi}{2}$ radians is equivalent to $90$ degrees. The sine of $90$ degrees is a well-known value in the unit circle, where the sine of an angle is the y-coordinate of the corresponding point on the unit circle.
Finding the point on the unit circle: At $90$ degrees or $\frac{\pi}{2}$ radians, the point on the unit circle is $(0, 1)$ . Therefore, the y-coordinate, which gives us the sine value, is $1$ .
Determining the sine value: Since the y-coordinate is $1$ , the value of $\sin\left(\frac{\pi}{2}\right)$ is $1$ . This corresponds to choice $(D)$ in the given options.