Solved on Jan 27, 2024

Find the $\csc$ of 270 degrees. Select the correct choice and, if necessary, provide the simplified answer.
A. $\csc 270^{\circ} = -1$ B. The function is undefined.

STEP 1

Assumptions
1. We are asked to find the value of the cosecant function at an angle of $270^{\circ}$ .
2. The cosecant function is the reciprocal of the sine function, i.e., $\csc(\theta) = \frac{1}{\sin(\theta)}$ .
3. The angle is given in degrees.

STEP 2

Recall the value of the sine function at $270^{\circ}$ .
$\sin(270^{\circ})$

STEP 3

The sine of $270^{\circ}$ is equal to $-1$ because at $270^{\circ}$ , the point on the unit circle is at the coordinates (0, -1).
$\sin(270^{\circ}) = -1$

STEP 4

Now, we find the cosecant of $270^{\circ}$ by taking the reciprocal of the sine of $270^{\circ}$ .
$\csc(270^{\circ}) = \frac{1}{\sin(270^{\circ})}$

STEP 5

Substitute the value of $\sin(270^{\circ})$ into the equation.
$\csc(270^{\circ}) = \frac{1}{-1}$

STEP 6

Calculate the value of $\csc(270^{\circ})$ .
$\csc(270^{\circ}) = -1$

STEP 7

Since we found a valid value for $\csc(270^{\circ})$ , it is not undefined.
The correct choice is A, and the value is:
$\csc 270^{\circ} = -1$

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Find the $\csc$ of 270 degrees. Select the correct choice and, if necessary, provide the simplified answer.
A. $\csc 270^{\circ} = -1$ B. The function is undefined.

STEP 1

Assumptions
1. We are asked to find the value of the cosecant function at an angle of $270^{\circ}$ .
2. The cosecant function is the reciprocal of the sine function, i.e., $\csc(\theta) = \frac{1}{\sin(\theta)}$ .
3. The angle is given in degrees.

STEP 2

Recall the value of the sine function at $270^{\circ}$ .
$\sin(270^{\circ})$

STEP 3

The sine of $270^{\circ}$ is equal to $-1$ because at $270^{\circ}$ , the point on the unit circle is at the coordinates (0, -1).
$\sin(270^{\circ}) = -1$

STEP 4

Now, we find the cosecant of $270^{\circ}$ by taking the reciprocal of the sine of $270^{\circ}$ .
$\csc(270^{\circ}) = \frac{1}{\sin(270^{\circ})}$

STEP 5

Substitute the value of $\sin(270^{\circ})$ into the equation.
$\csc(270^{\circ}) = \frac{1}{-1}$

STEP 6

Calculate the value of $\csc(270^{\circ})$ .
$\csc(270^{\circ}) = -1$

STEP 7

Since we found a valid value for $\csc(270^{\circ})$ , it is not undefined.
The correct choice is A, and the value is:
$\csc 270^{\circ} = -1$

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Find the csc⁡\csccsc of 270 degrees. Select the correct choice and, if necessary, provide the simplified answer.A. csc⁡270∘=−1\csc 270^{\circ} = -1csc270∘=−1 B. The function is undefined.

STEP 1

Assumptions1. We are asked to find the value of the cosecant function at an angle of 270∘270^{\circ}270∘.2. The cosecant function is the reciprocal of the sine function, i.e., csc⁡(θ)=1sin⁡(θ)\csc(\theta) = \frac{1}{\sin(\theta)}csc(θ)=sin(θ)1​.3. The angle is given in degrees.

STEP 2

Recall the value of the sine function at 270∘270^{\circ}270∘.sin⁡(270∘)\sin(270^{\circ})sin(270∘)

STEP 3

The sine of 270∘270^{\circ}270∘ is equal to −1-1−1 because at 270∘270^{\circ}270∘, the point on the unit circle is at the coordinates (0, -1).sin⁡(270∘)=−1\sin(270^{\circ}) = -1sin(270∘)=−1

STEP 4

Now, we find the cosecant of 270∘270^{\circ}270∘ by taking the reciprocal of the sine of 270∘270^{\circ}270∘.csc⁡(270∘)=1sin⁡(270∘)\csc(270^{\circ}) = \frac{1}{\sin(270^{\circ})}csc(270∘)=sin(270∘)1​

STEP 5

Substitute the value of sin⁡(270∘)\sin(270^{\circ})sin(270∘) into the equation.csc⁡(270∘)=1−1\csc(270^{\circ}) = \frac{1}{-1}csc(270∘)=−11​

STEP 6

Calculate the value of csc⁡(270∘)\csc(270^{\circ})csc(270∘).csc⁡(270∘)=−1\csc(270^{\circ}) = -1csc(270∘)=−1

STEP 7

Since we found a valid value for csc⁡(270∘)\csc(270^{\circ})csc(270∘), it is not undefined.The correct choice is A, and the value is:csc⁡270∘=−1\csc 270^{\circ} = -1csc270∘=−1

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Find the $\csc$ of 270 degrees. Select the correct choice and, if necessary, provide the simplified answer.
A. $\csc 270^{\circ} = -1$ B. The function is undefined.

Assumptions
1. We are asked to find the value of the cosecant function at an angle of $270^{\circ}$ .
2. The cosecant function is the reciprocal of the sine function, i.e., $\csc(\theta) = \frac{1}{\sin(\theta)}$ .
3. The angle is given in degrees.

Recall the value of the sine function at $270^{\circ}$ .
$\sin(270^{\circ})$

The sine of $270^{\circ}$ is equal to $-1$ because at $270^{\circ}$ , the point on the unit circle is at the coordinates (0, -1).
$\sin(270^{\circ}) = -1$

Now, we find the cosecant of $270^{\circ}$ by taking the reciprocal of the sine of $270^{\circ}$ .
$\csc(270^{\circ}) = \frac{1}{\sin(270^{\circ})}$

Substitute the value of $\sin(270^{\circ})$ into the equation.
$\csc(270^{\circ}) = \frac{1}{-1}$

Calculate the value of $\csc(270^{\circ})$ .
$\csc(270^{\circ}) = -1$

Since we found a valid value for $\csc(270^{\circ})$ , it is not undefined.
The correct choice is A, and the value is:
$\csc 270^{\circ} = -1$