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Popular >

solvefor w,P=4(Y/(Psin(w)))

Solution

solve for

w, P = 4 (\frac{Y}{P sin ( w )})

Solution

w = arcsin (\frac{4 Y}{P ^{2}}) + 2 πn, w = π + arcsin (- \frac{4 Y}{P ^{2}}) + 2 πn

Solution steps

P = 4 (\frac{Y}{P sin ( w )})

Switch sides

4 \cdot \frac{Y}{P sin ( w )} = P

Simplify

4 \cdot \frac{Y}{P sin ( w )} : \frac{4 Y}{P sin ( w )}

4 \cdot \frac{Y}{P sin ( w )}

Multiply fractions:

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

= \frac{Y \cdot 4}{P sin ( w )}

\frac{4 Y}{P sin ( w )} = P

Multiply both sides by

sin (w)

\frac{4 Y}{P sin ( w )} = P

Multiply both sides by

sin (w)

\frac{4 Y}{P sin ( w )} sin (w) = P sin (w)

Simplify

\frac{4 Y}{P} = P sin (w)

\frac{4 Y}{P} = P sin (w)

Switch sides

P sin (w) = \frac{4 Y}{P}

Divide both sides by

P; P \neq = 0

P sin (w) = \frac{4 Y}{P}

Divide both sides by

P; P \neq = 0

\frac{P sin ( w )}{P} = \frac{\frac{4 Y}{P}}{P}; P \neq = 0

Simplify

\frac{P sin ( w )}{P} = \frac{\frac{4 Y}{P}}{P}

Simplify

\frac{P sin ( w )}{P} : sin (w)

\frac{P sin ( w )}{P}

Cancel the common factor:

P

= sin (w)

Simplify

\frac{\frac{4 Y}{P}}{P} : \frac{4 Y}{P ^{2}}

\frac{\frac{4 Y}{P}}{P}

Apply the fraction rule:

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

= \frac{4 Y}{PP}

PP = P^{2}

PP

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

PP = P^{1 + 1}

= P^{1 + 1}

Add the numbers:

1 + 1 = 2

= P^{2}

= \frac{4 Y}{P ^{2}}

sin (w) = \frac{4 Y}{P ^{2}}; P \neq = 0

sin (w) = \frac{4 Y}{P ^{2}}; P \neq = 0

sin (w) = \frac{4 Y}{P ^{2}}; P \neq = 0

Apply trig inverse properties

sin (w) = \frac{4 Y}{P ^{2}}

General solutions for

sin (w) = \frac{4 Y}{P ^{2}}

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

w = arcsin (\frac{4 Y}{P ^{2}}) + 2 πn, w = π + arcsin (- \frac{4 Y}{P ^{2}}) + 2 πn

w = arcsin (\frac{4 Y}{P ^{2}}) + 2 πn, w = π + arcsin (- \frac{4 Y}{P ^{2}}) + 2 πn

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