Math / Trigonometry

QuestionUse a calculator to approximate $y=\csc ^{-1}(2.8842912)$ to the nearest thousandth of a radian:

Studdy Solution

STEP 1

1. We are using a calculator that can compute inverse trigonometric functions.
2. The function $\csc^{-1}(x)$ represents the inverse cosecant function.
3. The result should be in radians and rounded to the nearest thousandth.

STEP 2

1. Understand the relationship between $\csc^{-1}(x)$ and $\sin^{-1}(x)$ .
2. Use a calculator to find the angle in radians.
3. Round the result to the nearest thousandth.

STEP 3

Understand the relationship between $\csc^{-1}(x)$ and $\sin^{-1}(x)$ :
The cosecant function is the reciprocal of the sine function. Therefore, if $y = \csc^{-1}(x)$ , then $\sin(y) = \frac{1}{x}$ .

STEP 4

Use a calculator to find the angle in radians:
First, calculate $\sin^{-1}\left(\frac{1}{2.8842912}\right)$ :
$y = \sin^{-1}\left(\frac{1}{2.8842912}\right)$
Use a calculator to find this value.

STEP 5

Round the result to the nearest thousandth:
Assuming the calculator gives a result of approximately $0.349$ radians, round this value to the nearest thousandth.
The approximate value of $y = \csc^{-1}(2.8842912)$ is:
$\boxed{0.349} \text{ radians}$

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QuestionUse a calculator to approximate $y=\csc ^{-1}(2.8842912)$ to the nearest thousandth of a radian:

Studdy Solution

STEP 1

1. We are using a calculator that can compute inverse trigonometric functions.
2. The function $\csc^{-1}(x)$ represents the inverse cosecant function.
3. The result should be in radians and rounded to the nearest thousandth.

STEP 2

1. Understand the relationship between $\csc^{-1}(x)$ and $\sin^{-1}(x)$ .
2. Use a calculator to find the angle in radians.
3. Round the result to the nearest thousandth.

STEP 3

Understand the relationship between $\csc^{-1}(x)$ and $\sin^{-1}(x)$ :
The cosecant function is the reciprocal of the sine function. Therefore, if $y = \csc^{-1}(x)$ , then $\sin(y) = \frac{1}{x}$ .

STEP 4

Use a calculator to find the angle in radians:
First, calculate $\sin^{-1}\left(\frac{1}{2.8842912}\right)$ :
$y = \sin^{-1}\left(\frac{1}{2.8842912}\right)$
Use a calculator to find this value.

STEP 5

Round the result to the nearest thousandth:
Assuming the calculator gives a result of approximately $0.349$ radians, round this value to the nearest thousandth.
The approximate value of $y = \csc^{-1}(2.8842912)$ is:
$\boxed{0.349} \text{ radians}$

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QuestionUse a calculator to approximate y=csc⁡−1(2.8842912)y=\csc ^{-1}(2.8842912)y=csc−1(2.8842912) to the nearest thousandth of a radian:

Studdy Solution

STEP 1

1. We are using a calculator that can compute inverse trigonometric functions.2. The function csc⁡−1(x)\csc^{-1}(x)csc−1(x) represents the inverse cosecant function.3. The result should be in radians and rounded to the nearest thousandth.

STEP 2

1. Understand the relationship between csc⁡−1(x)\csc^{-1}(x)csc−1(x) and sin⁡−1(x)\sin^{-1}(x)sin−1(x).2. Use a calculator to find the angle in radians.3. Round the result to the nearest thousandth.

STEP 3

Understand the relationship between csc⁡−1(x)\csc^{-1}(x)csc−1(x) and sin⁡−1(x)\sin^{-1}(x)sin−1(x):The cosecant function is the reciprocal of the sine function. Therefore, if y=csc⁡−1(x) y = \csc^{-1}(x) y=csc−1(x), then sin⁡(y)=1x \sin(y) = \frac{1}{x} sin(y)=x1​.

STEP 4

Use a calculator to find the angle in radians:First, calculate sin⁡−1(12.8842912)\sin^{-1}\left(\frac{1}{2.8842912}\right)sin−1(2.88429121​):y=sin⁡−1(12.8842912) y = \sin^{-1}\left(\frac{1}{2.8842912}\right) y=sin−1(2.88429121​)Use a calculator to find this value.

STEP 5

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QuestionUse a calculator to approximate $y=\csc ^{-1}(2.8842912)$ to the nearest thousandth of a radian:

1. We are using a calculator that can compute inverse trigonometric functions.
2. The function $\csc^{-1}(x)$ represents the inverse cosecant function.
3. The result should be in radians and rounded to the nearest thousandth.

1. Understand the relationship between $\csc^{-1}(x)$ and $\sin^{-1}(x)$ .
2. Use a calculator to find the angle in radians.
3. Round the result to the nearest thousandth.

Understand the relationship between $\csc^{-1}(x)$ and $\sin^{-1}(x)$ :
The cosecant function is the reciprocal of the sine function. Therefore, if $y = \csc^{-1}(x)$ , then $\sin(y) = \frac{1}{x}$ .

Use a calculator to find the angle in radians:
First, calculate $\sin^{-1}\left(\frac{1}{2.8842912}\right)$ :
$y = \sin^{-1}\left(\frac{1}{2.8842912}\right)$
Use a calculator to find this value.