Math / Trigonometry

QuestionQuestion 8 (1 point) The exact radian measure for an angle of $135^{\circ}$ is a) $\pi$ b) $\frac{\pi}{2}$ c) $\frac{3 \pi}{4}$ d) $\frac{\pi}{4}$

Studdy Solution

STEP 1

1. We are converting an angle from degrees to radians.
2. The conversion factor between degrees and radians is $\pi$ radians = $180^\circ$ .

STEP 2

1. Use the conversion factor to convert $135^\circ$ to radians.
2. Simplify the expression to find the exact radian measure.
3. Compare the result with the given options.

STEP 3

To convert degrees to radians, use the formula:
$\text{Radians} = \text{Degrees} \times \frac{\pi}{180}$
Apply this formula to $135^\circ$ :
$135^\circ \times \frac{\pi}{180}$

STEP 4

Simplify the expression:
$135 \times \frac{\pi}{180} = \frac{135\pi}{180}$
Reduce the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 45:
$\frac{135\pi}{180} = \frac{3\pi}{4}$

STEP 5

Compare the simplified radian measure $\frac{3\pi}{4}$ with the given options:
a) $\pi$ b) $\frac{\pi}{2}$ c) $\frac{3\pi}{4}$ d) $\frac{\pi}{4}$
The correct answer is option c) $\frac{3\pi}{4}$ .
The exact radian measure for an angle of $135^\circ$ is:
$\boxed{\frac{3\pi}{4}}$

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QuestionQuestion 8 (1 point) The exact radian measure for an angle of $135^{\circ}$ is a) $\pi$ b) $\frac{\pi}{2}$ c) $\frac{3 \pi}{4}$ d) $\frac{\pi}{4}$

Studdy Solution

STEP 1

1. We are converting an angle from degrees to radians.
2. The conversion factor between degrees and radians is $\pi$ radians = $180^\circ$ .

STEP 2

1. Use the conversion factor to convert $135^\circ$ to radians.
2. Simplify the expression to find the exact radian measure.
3. Compare the result with the given options.

STEP 3

To convert degrees to radians, use the formula:
$\text{Radians} = \text{Degrees} \times \frac{\pi}{180}$
Apply this formula to $135^\circ$ :
$135^\circ \times \frac{\pi}{180}$

STEP 4

Simplify the expression:
$135 \times \frac{\pi}{180} = \frac{135\pi}{180}$
Reduce the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 45:
$\frac{135\pi}{180} = \frac{3\pi}{4}$

STEP 5

Compare the simplified radian measure $\frac{3\pi}{4}$ with the given options:
a) $\pi$ b) $\frac{\pi}{2}$ c) $\frac{3\pi}{4}$ d) $\frac{\pi}{4}$
The correct answer is option c) $\frac{3\pi}{4}$ .
The exact radian measure for an angle of $135^\circ$ is:
$\boxed{\frac{3\pi}{4}}$

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QuestionQuestion 8 (1 point) The exact radian measure for an angle of 135∘135^{\circ}135∘ is a) π\piπ b) π2\frac{\pi}{2}2π​ c) 3π4\frac{3 \pi}{4}43π​ d) π4\frac{\pi}{4}4π​

Studdy Solution

STEP 1

1. We are converting an angle from degrees to radians.2. The conversion factor between degrees and radians is π\piπ radians = 180∘180^\circ180∘.

STEP 2

1. Use the conversion factor to convert 135∘135^\circ135∘ to radians.2. Simplify the expression to find the exact radian measure.3. Compare the result with the given options.

STEP 3

To convert degrees to radians, use the formula:Radians=Degrees×π180\text{Radians} = \text{Degrees} \times \frac{\pi}{180}Radians=Degrees×180π​Apply this formula to 135∘135^\circ135∘:135∘×π180135^\circ \times \frac{\pi}{180}135∘×180π​

STEP 4

Simplify the expression:135×π180=135π180135 \times \frac{\pi}{180} = \frac{135\pi}{180}135×180π​=180135π​Reduce the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 45:135π180=3π4\frac{135\pi}{180} = \frac{3\pi}{4}180135π​=43π​

STEP 5

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QuestionQuestion 8 (1 point) The exact radian measure for an angle of $135^{\circ}$ is a) $\pi$ b) $\frac{\pi}{2}$ c) $\frac{3 \pi}{4}$ d) $\frac{\pi}{4}$

1. We are converting an angle from degrees to radians.
2. The conversion factor between degrees and radians is $\pi$ radians = $180^\circ$ .

1. Use the conversion factor to convert $135^\circ$ to radians.
2. Simplify the expression to find the exact radian measure.
3. Compare the result with the given options.

To convert degrees to radians, use the formula:
$\text{Radians} = \text{Degrees} \times \frac{\pi}{180}$
Apply this formula to $135^\circ$ :
$135^\circ \times \frac{\pi}{180}$

Simplify the expression:
$135 \times \frac{\pi}{180} = \frac{135\pi}{180}$
Reduce the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 45:
$\frac{135\pi}{180} = \frac{3\pi}{4}$