Solved on Jan 17, 2024

Find the value of $\frac{\pi}{2}-\frac{3 \pi}{10}$ .

STEP 1

Assumptions
1. We are given the expression $\frac{\pi}{2}-\frac{3\pi}{10}$ .
2. We need to simplify the expression.

STEP 2

To subtract the fractions, we need a common denominator. The least common multiple of the denominators 2 and 10 is 10.

STEP 3

Convert the first fraction $\frac{\pi}{2}$ to have the denominator 10.
$\frac{\pi}{2} = \frac{\pi}{2} \times \frac{5}{5} = \frac{5\pi}{10}$

STEP 4

Now we have two fractions with the same denominator, which allows us to subtract them directly.
$\frac{5\pi}{10} - \frac{3\pi}{10}$

STEP 5

Subtract the numerators while keeping the denominator the same.
$\frac{5\pi - 3\pi}{10}$

STEP 6

Perform the subtraction in the numerator.
$\frac{2\pi}{10}$

STEP 7

Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
$\frac{2\pi}{10} = \frac{\pi}{5}$
The simplified expression is $\frac{\pi}{5}$ .

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Find the value of $\frac{\pi}{2}-\frac{3 \pi}{10}$ .

STEP 1

Assumptions
1. We are given the expression $\frac{\pi}{2}-\frac{3\pi}{10}$ .
2. We need to simplify the expression.

STEP 2

To subtract the fractions, we need a common denominator. The least common multiple of the denominators 2 and 10 is 10.

STEP 3

Convert the first fraction $\frac{\pi}{2}$ to have the denominator 10.
$\frac{\pi}{2} = \frac{\pi}{2} \times \frac{5}{5} = \frac{5\pi}{10}$

STEP 4

Now we have two fractions with the same denominator, which allows us to subtract them directly.
$\frac{5\pi}{10} - \frac{3\pi}{10}$

STEP 5

Subtract the numerators while keeping the denominator the same.
$\frac{5\pi - 3\pi}{10}$

STEP 6

Perform the subtraction in the numerator.
$\frac{2\pi}{10}$

STEP 7

Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
$\frac{2\pi}{10} = \frac{\pi}{5}$
The simplified expression is $\frac{\pi}{5}$ .

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Find the value of π2−3π10\frac{\pi}{2}-\frac{3 \pi}{10}2π​−103π​.

STEP 1

Assumptions1. We are given the expression π2−3π10\frac{\pi}{2}-\frac{3\pi}{10}2π​−103π​.2. We need to simplify the expression.

STEP 2

To subtract the fractions, we need a common denominator. The least common multiple of the denominators 2 and 10 is 10.

STEP 3

Convert the first fraction π2\frac{\pi}{2}2π​ to have the denominator 10.π2=π2×55=5π10\frac{\pi}{2} = \frac{\pi}{2} \times \frac{5}{5} = \frac{5\pi}{10}2π​=2π​×55​=105π​

STEP 4

Now we have two fractions with the same denominator, which allows us to subtract them directly.5π10−3π10\frac{5\pi}{10} - \frac{3\pi}{10}105π​−103π​

STEP 5

Subtract the numerators while keeping the denominator the same.5π−3π10\frac{5\pi - 3\pi}{10}105π−3π​

STEP 6

Perform the subtraction in the numerator.2π10\frac{2\pi}{10}102π​

STEP 7

Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2.2π10=π5\frac{2\pi}{10} = \frac{\pi}{5}102π​=5π​The simplified expression is π5\frac{\pi}{5}5π​.

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Find the value of $\frac{\pi}{2}-\frac{3 \pi}{10}$ .

Assumptions
1. We are given the expression $\frac{\pi}{2}-\frac{3\pi}{10}$ .
2. We need to simplify the expression.

Convert the first fraction $\frac{\pi}{2}$ to have the denominator 10.
$\frac{\pi}{2} = \frac{\pi}{2} \times \frac{5}{5} = \frac{5\pi}{10}$

Now we have two fractions with the same denominator, which allows us to subtract them directly.
$\frac{5\pi}{10} - \frac{3\pi}{10}$

Subtract the numerators while keeping the denominator the same.
$\frac{5\pi - 3\pi}{10}$

Perform the subtraction in the numerator.
$\frac{2\pi}{10}$

Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
$\frac{2\pi}{10} = \frac{\pi}{5}$
The simplified expression is $\frac{\pi}{5}$ .