Math / Trigonometry

QuestionAnswer the following. (a) Find an angle between $0^{\circ}$ and $360^{\circ}$ that is coterminal with $1170^{\circ}$ . (b) Find an angle between 0 and $2 \pi$ that is coterminal with $-\frac{17 \pi}{10}$ .
Give exact values for your answers. (a) $\square$ 。 (b) $\square$ radians

Studdy Solution

STEP 1

1. Coterminal angles differ by full rotations.
2. A full rotation in degrees is $360^\circ$ .
3. A full rotation in radians is $2\pi$ .

STEP 2

1. Find a coterminal angle in degrees.
2. Find a coterminal angle in radians.

STEP 3

To find an angle between $0^\circ$ and $360^\circ$ that is coterminal with $1170^\circ$ , we need to subtract $360^\circ$ repeatedly until the result is within the desired range.

STEP 4

Calculate the coterminal angle: $1170^\circ - 360^\circ \times n$ where $n$ is the number of full rotations. We start by dividing: $n = \left\lfloor \frac{1170}{360} \right\rfloor = 3$

STEP 5

Subtract $3 \times 360^\circ$ from $1170^\circ$ : $1170^\circ - 1080^\circ = 90^\circ$

STEP 6

To find an angle between $0$ and $2\pi$ that is coterminal with $-\frac{17\pi}{10}$ , we need to add $2\pi$ repeatedly until the result is within the desired range.

STEP 7

Calculate the coterminal angle: $-\frac{17\pi}{10} + 2\pi \times n$ where $n$ is the number of full rotations. We start by finding $n$ such that the angle is positive: $n = \left\lceil \frac{17}{10} \right\rceil = 2$

STEP 8

Add $2 \times 2\pi$ to $-\frac{17\pi}{10}$ : $-\frac{17\pi}{10} + \frac{20\pi}{10} = \frac{3\pi}{10}$
The exact values for the coterminal angles are: (a) $\boxed{90^\circ}$ (b) $\boxed{\frac{3\pi}{10}}$ radians

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QuestionAnswer the following. (a) Find an angle between $0^{\circ}$ and $360^{\circ}$ that is coterminal with $1170^{\circ}$ . (b) Find an angle between 0 and $2 \pi$ that is coterminal with $-\frac{17 \pi}{10}$ .
Give exact values for your answers. (a) $\square$ 。 (b) $\square$ radians

Studdy Solution

STEP 1

1. Coterminal angles differ by full rotations.
2. A full rotation in degrees is $360^\circ$ .
3. A full rotation in radians is $2\pi$ .

STEP 2

1. Find a coterminal angle in degrees.
2. Find a coterminal angle in radians.

STEP 3

To find an angle between $0^\circ$ and $360^\circ$ that is coterminal with $1170^\circ$ , we need to subtract $360^\circ$ repeatedly until the result is within the desired range.

STEP 4

Calculate the coterminal angle: $1170^\circ - 360^\circ \times n$ where $n$ is the number of full rotations. We start by dividing: $n = \left\lfloor \frac{1170}{360} \right\rfloor = 3$

STEP 5

Subtract $3 \times 360^\circ$ from $1170^\circ$ : $1170^\circ - 1080^\circ = 90^\circ$

STEP 6

To find an angle between $0$ and $2\pi$ that is coterminal with $-\frac{17\pi}{10}$ , we need to add $2\pi$ repeatedly until the result is within the desired range.

STEP 7

Calculate the coterminal angle: $-\frac{17\pi}{10} + 2\pi \times n$ where $n$ is the number of full rotations. We start by finding $n$ such that the angle is positive: $n = \left\lceil \frac{17}{10} \right\rceil = 2$

STEP 8

Add $2 \times 2\pi$ to $-\frac{17\pi}{10}$ : $-\frac{17\pi}{10} + \frac{20\pi}{10} = \frac{3\pi}{10}$
The exact values for the coterminal angles are: (a) $\boxed{90^\circ}$ (b) $\boxed{\frac{3\pi}{10}}$ radians

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Studdy Solution

STEP 1

1. Coterminal angles differ by full rotations.2. A full rotation in degrees is 360∘ 360^\circ 360∘.3. A full rotation in radians is 2π 2\pi 2π.

STEP 2

1. Find a coterminal angle in degrees.2. Find a coterminal angle in radians.

STEP 3

To find an angle between 0∘ 0^\circ 0∘ and 360∘ 360^\circ 360∘ that is coterminal with 1170∘ 1170^\circ 1170∘, we need to subtract 360∘ 360^\circ 360∘ repeatedly until the result is within the desired range.

STEP 4

Calculate the coterminal angle: 1170∘−360∘×n 1170^\circ - 360^\circ \times n 1170∘−360∘×n where n n n is the number of full rotations. We start by dividing: n=⌊1170360⌋=3 n = \left\lfloor \frac{1170}{360} \right\rfloor = 3 n=⌊3601170​⌋=3

STEP 5

Subtract 3×360∘ 3 \times 360^\circ 3×360∘ from 1170∘ 1170^\circ 1170∘: 1170∘−1080∘=90∘ 1170^\circ - 1080^\circ = 90^\circ 1170∘−1080∘=90∘

STEP 6

To find an angle between 0 0 0 and 2π 2\pi 2π that is coterminal with −17π10 -\frac{17\pi}{10} −1017π​, we need to add 2π 2\pi 2π repeatedly until the result is within the desired range.

STEP 7

Calculate the coterminal angle: −17π10+2π×n -\frac{17\pi}{10} + 2\pi \times n −1017π​+2π×n where n n n is the number of full rotations. We start by finding n n n such that the angle is positive: n=⌈1710⌉=2 n = \left\lceil \frac{17}{10} \right\rceil = 2 n=⌈1017​⌉=2

STEP 8

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1. Coterminal angles differ by full rotations.
2. A full rotation in degrees is $360^\circ$ .
3. A full rotation in radians is $2\pi$ .

1. Find a coterminal angle in degrees.
2. Find a coterminal angle in radians.

To find an angle between $0^\circ$ and $360^\circ$ that is coterminal with $1170^\circ$ , we need to subtract $360^\circ$ repeatedly until the result is within the desired range.

Calculate the coterminal angle: $1170^\circ - 360^\circ \times n$ where $n$ is the number of full rotations. We start by dividing: $n = \left\lfloor \frac{1170}{360} \right\rfloor = 3$

Subtract $3 \times 360^\circ$ from $1170^\circ$ : $1170^\circ - 1080^\circ = 90^\circ$

To find an angle between $0$ and $2\pi$ that is coterminal with $-\frac{17\pi}{10}$ , we need to add $2\pi$ repeatedly until the result is within the desired range.

Calculate the coterminal angle: $-\frac{17\pi}{10} + 2\pi \times n$ where $n$ is the number of full rotations. We start by finding $n$ such that the angle is positive: $n = \left\lceil \frac{17}{10} \right\rceil = 2$