QuestionFind the exact value of $\sin(13 \pi)$ without using a calculator.

Studdy Solution

STEP 1

Assumptions1. We are working with the unit circle where the sine function gives the y-coordinate of a point on the circle. . We are working in radians, not degrees.

STEP 2

The sine function has a period of $2\pi$ . This means that $\sin(x) = \sin(x +2n\pi)$ , where $n$ is any integer. We can use this property to simplify the argument of the sine function.

STEP 3

We can write $13\pi$ as $12\pi + \pi$ .

STEP 4

Since the sine function has a period of $2\pi$ , we know that $\sin(12\pi + \pi) = \sin(\pi)$ .

STEP 5

The value of $\sin(\pi)$ is0.
So, $\sin(13\pi) =0$ .

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QuestionFind the exact value of $\sin(13 \pi)$ without using a calculator.

Studdy Solution

STEP 1

Assumptions1. We are working with the unit circle where the sine function gives the y-coordinate of a point on the circle. . We are working in radians, not degrees.

STEP 2

The sine function has a period of $2\pi$ . This means that $\sin(x) = \sin(x +2n\pi)$ , where $n$ is any integer. We can use this property to simplify the argument of the sine function.

STEP 3

We can write $13\pi$ as $12\pi + \pi$ .

STEP 4

Since the sine function has a period of $2\pi$ , we know that $\sin(12\pi + \pi) = \sin(\pi)$ .

STEP 5

The value of $\sin(\pi)$ is0.
So, $\sin(13\pi) =0$ .

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QuestionFind the exact value of sin⁡(13π)\sin(13 \pi)sin(13π) without using a calculator.

Studdy Solution

STEP 1

Assumptions1. We are working with the unit circle where the sine function gives the y-coordinate of a point on the circle. . We are working in radians, not degrees.

STEP 2

The sine function has a period of 2π2\pi2π. This means that sin⁡(x)=sin⁡(x+2nπ)\sin(x) = \sin(x +2n\pi)sin(x)=sin(x+2nπ), where nnn is any integer. We can use this property to simplify the argument of the sine function.

STEP 3

We can write 13π13\pi13π as 12π+π12\pi + \pi12π+π.

STEP 4

Since the sine function has a period of 2π2\pi2π, we know that sin⁡(12π+π)=sin⁡(π)\sin(12\pi + \pi) = \sin(\pi)sin(12π+π)=sin(π).

STEP 5

The value of sin⁡(π)\sin(\pi)sin(π) is0.So, sin⁡(13π)=0\sin(13\pi) =0sin(13π)=0.

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QuestionFind the exact value of $\sin(13 \pi)$ without using a calculator.

The sine function has a period of $2\pi$ . This means that $\sin(x) = \sin(x +2n\pi)$ , where $n$ is any integer. We can use this property to simplify the argument of the sine function.

We can write $13\pi$ as $12\pi + \pi$ .

Since the sine function has a period of $2\pi$ , we know that $\sin(12\pi + \pi) = \sin(\pi)$ .

The value of $\sin(\pi)$ is0.
So, $\sin(13\pi) =0$ .