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Popular Trigonometry >

14sin(20x)-3=2

Solution

14 sin (20 x) - 3 = 2

Solution

x = \frac{0.36520 \dots}{20} + \frac{πn}{10}, x = \frac{π}{20} - \frac{0.36520 \dots}{20} + \frac{πn}{10}

+1

Degrees

x = 1.04624 \dots^{\circ} + 1 8^{\circ} n, x = 7.95375 \dots^{\circ} + 1 8^{\circ} n

Solution steps

14 sin (20 x) - 3 = 2

Move

3

to the right side

14 sin (20 x) - 3 = 2

Add

3

to both sides

14 sin (20 x) - 3 + 3 = 2 + 3

Simplify

14 sin (20 x) = 5

14 sin (20 x) = 5

Divide both sides by

14

14 sin (20 x) = 5

Divide both sides by

14

\frac{14 sin ( 20 x )}{14} = \frac{5}{14}

Simplify

sin (20 x) = \frac{5}{14}

sin (20 x) = \frac{5}{14}

Apply trig inverse properties

sin (20 x) = \frac{5}{14}

General solutions for

sin (20 x) = \frac{5}{14}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

20 x = arcsin (\frac{5}{14}) + 2 πn, 20 x = π - arcsin (\frac{5}{14}) + 2 πn

20 x = arcsin (\frac{5}{14}) + 2 πn, 20 x = π - arcsin (\frac{5}{14}) + 2 πn

Solve

20 x = arcsin (\frac{5}{14}) + 2 πn : x = \frac{arcsin ( \frac{5}{14} )}{20} + \frac{πn}{10}

20 x = arcsin (\frac{5}{14}) + 2 πn

Divide both sides by

20

20 x = arcsin (\frac{5}{14}) + 2 πn

Divide both sides by

20

\frac{20 x}{20} = \frac{arcsin ( \frac{5}{14} )}{20} + \frac{2 πn}{20}

Simplify

x = \frac{arcsin ( \frac{5}{14} )}{20} + \frac{πn}{10}

x = \frac{arcsin ( \frac{5}{14} )}{20} + \frac{πn}{10}

Solve

20 x = π - arcsin (\frac{5}{14}) + 2 πn : x = \frac{π}{20} - \frac{arcsin ( \frac{5}{14} )}{20} + \frac{πn}{10}

20 x = π - arcsin (\frac{5}{14}) + 2 πn

Divide both sides by

20

20 x = π - arcsin (\frac{5}{14}) + 2 πn

Divide both sides by

20

\frac{20 x}{20} = \frac{π}{20} - \frac{arcsin ( \frac{5}{14} )}{20} + \frac{2 πn}{20}

Simplify

x = \frac{π}{20} - \frac{arcsin ( \frac{5}{14} )}{20} + \frac{πn}{10}

x = \frac{π}{20} - \frac{arcsin ( \frac{5}{14} )}{20} + \frac{πn}{10}

x = \frac{arcsin ( \frac{5}{14} )}{20} + \frac{πn}{10}, x = \frac{π}{20} - \frac{arcsin ( \frac{5}{14} )}{20} + \frac{πn}{10}

Show solutions in decimal form

x = \frac{0.36520 \dots}{20} + \frac{πn}{10}, x = \frac{π}{20} - \frac{0.36520 \dots}{20} + \frac{πn}{10}

Graph

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