What is the general solution for 2sin(1/2 x)=1,0<= x<= 12 ?

Q: What is the general solution for 2sin(1/2 x)=1,0<= x<= 12 ?

The general solution for 2sin(1/2 x)=1,0<= x<= 12 is No Solution for x\in\mathbb{R}

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2sin(1/2 x)=1,0<= x<= 12

Solution

2 sin (\frac{1}{2} x) = 1, 0^{\circ} \leq x \leq 1 2^{\circ}

Solution

No Solution for x \in R

Solution steps

2 sin (\frac{1}{2} x) = 1, 0^{\circ} \leq x \leq 1 2^{\circ}

Divide both sides by

2

2 sin (\frac{1}{2} x) = 1

Divide both sides by

2

\frac{2 sin ( \frac{1}{2} x )}{2} = \frac{1}{2}

Simplify

sin (\frac{1}{2} x) = \frac{1}{2}

sin (\frac{1}{2} x) = \frac{1}{2}

General solutions for

sin (\frac{1}{2} x) = \frac{1}{2}

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

\frac{1}{2} x = 3 0^{\circ} + 36 0^{\circ} n, \frac{1}{2} x = 15 0^{\circ} + 36 0^{\circ} n

\frac{1}{2} x = 3 0^{\circ} + 36 0^{\circ} n, \frac{1}{2} x = 15 0^{\circ} + 36 0^{\circ} n

Solve

\frac{1}{2} x = 3 0^{\circ} + 36 0^{\circ} n : x = 6 0^{\circ} + 72 0^{\circ} n

\frac{1}{2} x = 3 0^{\circ} + 36 0^{\circ} n

Multiply both sides by

2

\frac{1}{2} x = 3 0^{\circ} + 36 0^{\circ} n

Multiply both sides by

2

2 \cdot \frac{1}{2} x = 2 \cdot 3 0^{\circ} + 2 \cdot 36 0^{\circ} n

Simplify

2 \cdot \frac{1}{2} x = 2 \cdot 3 0^{\circ} + 2 \cdot 36 0^{\circ} n

Simplify

2 \cdot \frac{1}{2} x : x

2 \cdot \frac{1}{2} x

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 2}{2} x

Cancel the common factor:

2

= x \cdot 1

Multiply:

x \cdot 1 = x

= x

Simplify

2 \cdot 3 0^{\circ} + 2 \cdot 36 0^{\circ} n : 6 0^{\circ} + 72 0^{\circ} n

2 \cdot 3 0^{\circ} + 2 \cdot 36 0^{\circ} n

2 \cdot 3 0^{\circ} = 6 0^{\circ}

2 \cdot 3 0^{\circ}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= 6 0^{\circ}

Cancel the common factor:

2

= 6 0^{\circ}

2 \cdot 36 0^{\circ} n = 72 0^{\circ} n

2 \cdot 36 0^{\circ} n

Multiply the numbers:

2 \cdot 2 = 4

= 72 0^{\circ} n

= 6 0^{\circ} + 72 0^{\circ} n

x = 6 0^{\circ} + 72 0^{\circ} n

x = 6 0^{\circ} + 72 0^{\circ} n

x = 6 0^{\circ} + 72 0^{\circ} n

Solve

\frac{1}{2} x = 15 0^{\circ} + 36 0^{\circ} n : x = 30 0^{\circ} + 72 0^{\circ} n

\frac{1}{2} x = 15 0^{\circ} + 36 0^{\circ} n

Multiply both sides by

2

\frac{1}{2} x = 15 0^{\circ} + 36 0^{\circ} n

Multiply both sides by

2

2 \cdot \frac{1}{2} x = 2 \cdot 15 0^{\circ} + 2 \cdot 36 0^{\circ} n

Simplify

2 \cdot \frac{1}{2} x = 2 \cdot 15 0^{\circ} + 2 \cdot 36 0^{\circ} n

Simplify

2 \cdot \frac{1}{2} x : x

2 \cdot \frac{1}{2} x

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 2}{2} x

Cancel the common factor:

2

= x \cdot 1

Multiply:

x \cdot 1 = x

= x

Simplify

2 \cdot 15 0^{\circ} + 2 \cdot 36 0^{\circ} n : 30 0^{\circ} + 72 0^{\circ} n

2 \cdot 15 0^{\circ} + 2 \cdot 36 0^{\circ} n

2 \cdot 15 0^{\circ} = 30 0^{\circ}

2 \cdot 15 0^{\circ}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= 30 0^{\circ}

Multiply the numbers:

5 \cdot 2 = 10

= 30 0^{\circ}

Cancel the common factor:

2

= 30 0^{\circ}

2 \cdot 36 0^{\circ} n = 72 0^{\circ} n

2 \cdot 36 0^{\circ} n

Multiply the numbers:

2 \cdot 2 = 4

= 72 0^{\circ} n

= 30 0^{\circ} + 72 0^{\circ} n

x = 30 0^{\circ} + 72 0^{\circ} n

x = 30 0^{\circ} + 72 0^{\circ} n

x = 30 0^{\circ} + 72 0^{\circ} n

x = 6 0^{\circ} + 72 0^{\circ} n, x = 30 0^{\circ} + 72 0^{\circ} n

Solutions for the range

0 \leq x \leq 1 2^{\circ}

No Solution for x \in R

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 2sin(1/2 x)=1,0<= x<= 12 ?
The general solution for 2sin(1/2 x)=1,0<= x<= 12 is No Solution for x\in\mathbb{R}