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Popular >

solvefor x,csin(mx)m=(npi)/a

Solution

solve for

x, c sin (m x) m = \frac{nπ}{a}

Solution

x = \frac{arcsin ( \frac{πn}{c ma} )}{m} + \frac{2 πk}{m}, x = \frac{π}{m} + \frac{arcsin ( - \frac{πn}{c ma} )}{m} + \frac{2 πk}{m}

Solution steps

c sin (m x) m = \frac{nπ}{a}

Divide both sides by

c m; c \neq = 0

c sin (m x) m = \frac{nπ}{a}

Divide both sides by

c m; c \neq = 0

\frac{c sin ( m x ) m}{c m} = \frac{\frac{nπ}{a}}{c m}; c \neq = 0

Simplify

\frac{c sin ( m x ) m}{c m} = \frac{\frac{nπ}{a}}{c m}

Simplify

\frac{c sin ( m x ) m}{c m} : sin (m x)

\frac{c sin ( m x ) m}{c m}

Cancel the common factor:

c

= \frac{m sin ( m x )}{m}

Cancel the common factor:

m

= sin (m x)

Simplify

\frac{\frac{nπ}{a}}{c m} : \frac{πn}{c ma}

\frac{\frac{nπ}{a}}{c m}

Apply the fraction rule:

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

= \frac{nπ}{a c m}

sin (m x) = \frac{πn}{c ma}; c \neq = 0

sin (m x) = \frac{πn}{c ma}; c \neq = 0

sin (m x) = \frac{πn}{c ma}; c \neq = 0

Apply trig inverse properties

sin (m x) = \frac{πn}{c ma}

General solutions for

sin (m x) = \frac{πn}{c ma}

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

m x = arcsin (\frac{πn}{c ma}) + 2 πk, m x = π + arcsin (- \frac{πn}{c ma}) + 2 πk

m x = arcsin (\frac{πn}{c ma}) + 2 πk, m x = π + arcsin (- \frac{πn}{c ma}) + 2 πk

Solve

m x = arcsin (\frac{πn}{c ma}) + 2 πk : x = \frac{arcsin ( \frac{πn}{c ma} )}{m} + \frac{2 πk}{m}; m \neq = 0

m x = arcsin (\frac{πn}{c ma}) + 2 πk

Divide both sides by

m; m \neq = 0

m x = arcsin (\frac{πn}{c ma}) + 2 πk

Divide both sides by

m; m \neq = 0

\frac{m x}{m} = \frac{arcsin ( \frac{πn}{c ma} )}{m} + \frac{2 πk}{m}; m \neq = 0

Simplify

x = \frac{arcsin ( \frac{πn}{c ma} )}{m} + \frac{2 πk}{m}; m \neq = 0

x = \frac{arcsin ( \frac{πn}{c ma} )}{m} + \frac{2 πk}{m}; m \neq = 0

Solve

m x = π + arcsin (- \frac{πn}{c ma}) + 2 πk : x = \frac{π}{m} + \frac{arcsin ( - \frac{πn}{c ma} )}{m} + \frac{2 πk}{m}; m \neq = 0

m x = π + arcsin (- \frac{πn}{c ma}) + 2 πk

Divide both sides by

m; m \neq = 0

m x = π + arcsin (- \frac{πn}{c ma}) + 2 πk

Divide both sides by

m; m \neq = 0

\frac{m x}{m} = \frac{π}{m} + \frac{arcsin ( - \frac{πn}{c ma} )}{m} + \frac{2 πk}{m}; m \neq = 0

Simplify

x = \frac{π}{m} + \frac{arcsin ( - \frac{πn}{c ma} )}{m} + \frac{2 πk}{m}; m \neq = 0

x = \frac{π}{m} + \frac{arcsin ( - \frac{πn}{c ma} )}{m} + \frac{2 πk}{m}; m \neq = 0

x = \frac{arcsin ( \frac{πn}{c ma} )}{m} + \frac{2 πk}{m}, x = \frac{π}{m} + \frac{arcsin ( - \frac{πn}{c ma} )}{m} + \frac{2 πk}{m}

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