Math / Trigonometry

Question3. Convert between radians and degrees. Express answers exactly if possible, otherwise to a whole number of degrees or 3 decimal places for radians. [4 marks] a. $180^{\circ}$ b. 5 c. $13^{\circ}$ d. $\pi / 7$

Studdy Solution

STEP 1

1. The conversion between degrees and radians uses the relationship $180^\circ = \pi$ radians.
2. To convert degrees to radians, use the formula: $\text{radians} = \text{degrees} \times \frac{\pi}{180}$ .
3. To convert radians to degrees, use the formula: $\text{degrees} = \text{radians} \times \frac{180}{\pi}$ .

STEP 2

1. Convert degrees to radians.
2. Convert radians to degrees.

STEP 3

Convert $180^\circ$ to radians.
Using the conversion formula:
$\text{radians} = 180^\circ \times \frac{\pi}{180} = \pi$

STEP 4

Convert 5 radians to degrees.
Using the conversion formula:
$\text{degrees} = 5 \times \frac{180}{\pi}$
Calculate the value:
$\text{degrees} \approx 5 \times 57.2958 \approx 286.479$
Rounded to a whole number:
$\text{degrees} = 286$

STEP 5

Convert $13^\circ$ to radians.
Using the conversion formula:
$\text{radians} = 13^\circ \times \frac{\pi}{180}$
Calculate the value:
$\text{radians} = \frac{13\pi}{180}$

STEP 6

Convert $\frac{\pi}{7}$ radians to degrees.
Using the conversion formula:
$\text{degrees} = \frac{\pi}{7} \times \frac{180}{\pi}$
Calculate the value:
$\text{degrees} = \frac{180}{7} \approx 25.714$
Rounded to three decimal places:
$\text{degrees} = 25.714$
The converted values are: a. $180^\circ = \pi$ radians b. 5 radians $\approx 286$ degrees c. $13^\circ = \frac{13\pi}{180}$ radians d. $\frac{\pi}{7}$ radians $\approx 25.714$ degrees

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Question3. Convert between radians and degrees. Express answers exactly if possible, otherwise to a whole number of degrees or 3 decimal places for radians. [4 marks] a. $180^{\circ}$ b. 5 c. $13^{\circ}$ d. $\pi / 7$

Studdy Solution

STEP 1

STEP 2

1. Convert degrees to radians.
2. Convert radians to degrees.

STEP 3

Convert $180^\circ$ to radians.
Using the conversion formula:
$\text{radians} = 180^\circ \times \frac{\pi}{180} = \pi$

STEP 4

Convert 5 radians to degrees.
Using the conversion formula:
$\text{degrees} = 5 \times \frac{180}{\pi}$
Calculate the value:
$\text{degrees} \approx 5 \times 57.2958 \approx 286.479$
Rounded to a whole number:
$\text{degrees} = 286$

STEP 5

Convert $13^\circ$ to radians.
Using the conversion formula:
$\text{radians} = 13^\circ \times \frac{\pi}{180}$
Calculate the value:
$\text{radians} = \frac{13\pi}{180}$

STEP 6

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Question3. Convert between radians and degrees. Express answers exactly if possible, otherwise to a whole number of degrees or 3 decimal places for radians. [4 marks] a. 180∘180^{\circ}180∘ b. 5 c. 13∘13^{\circ}13∘ d. π/7\pi / 7π/7

Studdy Solution

STEP 1

STEP 2

1. Convert degrees to radians.2. Convert radians to degrees.

STEP 3

Convert 180∘ 180^\circ 180∘ to radians.Using the conversion formula:radians=180∘×π180=π \text{radians} = 180^\circ \times \frac{\pi}{180} = \pi radians=180∘×180π​=π

STEP 4

STEP 5

Convert 13∘ 13^\circ 13∘ to radians.Using the conversion formula:radians=13∘×π180 \text{radians} = 13^\circ \times \frac{\pi}{180} radians=13∘×180π​Calculate the value:radians=13π180 \text{radians} = \frac{13\pi}{180} radians=18013π​

STEP 6

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Question3. Convert between radians and degrees. Express answers exactly if possible, otherwise to a whole number of degrees or 3 decimal places for radians. [4 marks] a. $180^{\circ}$ b. 5 c. $13^{\circ}$ d. $\pi / 7$

1. Convert degrees to radians.
2. Convert radians to degrees.

Convert $180^\circ$ to radians.
Using the conversion formula:
$\text{radians} = 180^\circ \times \frac{\pi}{180} = \pi$

Convert $13^\circ$ to radians.
Using the conversion formula:
$\text{radians} = 13^\circ \times \frac{\pi}{180}$
Calculate the value:
$\text{radians} = \frac{13\pi}{180}$