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Popular >

solvefor y,(sin(7y))/7 =(cos(2x))/2+1/2

Solution

solve for

y, \frac{sin ( 7 y )}{7} = \frac{cos ( 2 x )}{2} + \frac{1}{2}

Solution

y = \frac{arcsin ( \frac{7 c o s ( 2 x ) + 7}{2} )}{7} + \frac{2 πn}{7}, y = \frac{π}{7} + \frac{arcsin ( - \frac{7 c o s ( 2 x ) + 7}{2} )}{7} + \frac{2 πn}{7}

Solution steps

\frac{sin ( 7 y )}{7} = \frac{cos ( 2 x )}{2} + \frac{1}{2}

Multiply both sides by

7

\frac{sin ( 7 y )}{7} = \frac{cos ( 2 x )}{2} + \frac{1}{2}

Multiply both sides by

7

\frac{7 sin ( 7 y )}{7} = 7 \cdot \frac{cos ( 2 x )}{2} + 7 \cdot \frac{1}{2}

Simplify

\frac{7 sin ( 7 y )}{7} = 7 \cdot \frac{cos ( 2 x )}{2} + 7 \cdot \frac{1}{2}

Simplify

\frac{7 sin ( 7 y )}{7} : sin (7 y)

\frac{7 sin ( 7 y )}{7}

Divide the numbers:

\frac{7}{7} = 1

= sin (7 y)

Simplify

7 \cdot \frac{cos ( 2 x )}{2} + 7 \cdot \frac{1}{2} : \frac{7 cos ( 2 x ) + 7}{2}

7 \cdot \frac{cos ( 2 x )}{2} + 7 \cdot \frac{1}{2}

7 \cdot \frac{cos ( 2 x )}{2} = \frac{7 cos ( 2 x )}{2}

7 \cdot \frac{cos ( 2 x )}{2}

Multiply fractions:

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

= \frac{cos ( 2 x ) \cdot 7}{2}

7 \cdot \frac{1}{2} = \frac{7}{2}

7 \cdot \frac{1}{2}

Multiply fractions:

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

= \frac{1 \cdot 7}{2}

Multiply the numbers:

1 \cdot 7 = 7

= \frac{7}{2}

= \frac{7 cos ( 2 x )}{2} + \frac{7}{2}

Apply rule

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

= \frac{7 cos ( 2 x ) + 7}{2}

sin (7 y) = \frac{7 cos ( 2 x ) + 7}{2}

sin (7 y) = \frac{7 cos ( 2 x ) + 7}{2}

sin (7 y) = \frac{7 cos ( 2 x ) + 7}{2}

Apply trig inverse properties

sin (7 y) = \frac{7 cos ( 2 x ) + 7}{2}

General solutions for

sin (7 y) = \frac{7 cos ( 2 x ) + 7}{2}

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

7 y = arcsin (\frac{7 cos ( 2 x ) + 7}{2}) + 2 πn, 7 y = π + arcsin (- \frac{7 cos ( 2 x ) + 7}{2}) + 2 πn

7 y = arcsin (\frac{7 cos ( 2 x ) + 7}{2}) + 2 πn, 7 y = π + arcsin (- \frac{7 cos ( 2 x ) + 7}{2}) + 2 πn

Solve

7 y = arcsin (\frac{7 cos ( 2 x ) + 7}{2}) + 2 πn : y = \frac{arcsin ( \frac{7 c o s ( 2 x ) + 7}{2} )}{7} + \frac{2 πn}{7}

7 y = arcsin (\frac{7 cos ( 2 x ) + 7}{2}) + 2 πn

Divide both sides by

7

7 y = arcsin (\frac{7 cos ( 2 x ) + 7}{2}) + 2 πn

Divide both sides by

7

\frac{7 y}{7} = \frac{arcsin ( \frac{7 c o s ( 2 x ) + 7}{2} )}{7} + \frac{2 πn}{7}

Simplify

y = \frac{arcsin ( \frac{7 c o s ( 2 x ) + 7}{2} )}{7} + \frac{2 πn}{7}

y = \frac{arcsin ( \frac{7 c o s ( 2 x ) + 7}{2} )}{7} + \frac{2 πn}{7}

Solve

7 y = π + arcsin (- \frac{7 cos ( 2 x ) + 7}{2}) + 2 πn : y = \frac{π}{7} + \frac{arcsin ( - \frac{7 c o s ( 2 x ) + 7}{2} )}{7} + \frac{2 πn}{7}

7 y = π + arcsin (- \frac{7 cos ( 2 x ) + 7}{2}) + 2 πn

Divide both sides by

7

7 y = π + arcsin (- \frac{7 cos ( 2 x ) + 7}{2}) + 2 πn

Divide both sides by

7

\frac{7 y}{7} = \frac{π}{7} + \frac{arcsin ( - \frac{7 c o s ( 2 x ) + 7}{2} )}{7} + \frac{2 πn}{7}

Simplify

y = \frac{π}{7} + \frac{arcsin ( - \frac{7 c o s ( 2 x ) + 7}{2} )}{7} + \frac{2 πn}{7}

y = \frac{π}{7} + \frac{arcsin ( - \frac{7 c o s ( 2 x ) + 7}{2} )}{7} + \frac{2 πn}{7}

y = \frac{arcsin ( \frac{7 c o s ( 2 x ) + 7}{2} )}{7} + \frac{2 πn}{7}, y = \frac{π}{7} + \frac{arcsin ( - \frac{7 c o s ( 2 x ) + 7}{2} )}{7} + \frac{2 πn}{7}

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