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Popular >

solvefor x,T(7)=3.15cos(pi/6 x)+19.15

Solution

solve for

x, T (7) = 3.15 cos (\frac{π}{6} x) + 19.15

Solution

x = \frac{6 arccos ( \frac{140 T - 383}{63} )}{π} + 12 n, x = - \frac{6 arccos ( \frac{140 T - 383}{63} )}{π} + 12 n

Solution steps

T (7) = 3.15 cos (\frac{π}{6} x) + 19.15

Switch sides

3.15 cos (\frac{π}{6} x) + 19.15 = T \cdot 7

Multiply both sides by

100

315 cos (\frac{π}{6} x) + 1915 = 700 T

Move

1915

to the right side

315 cos (\frac{π}{6} x) = 700 T - 1915

Divide both sides by

315

cos (\frac{π}{6} x) = \frac{140 T - 383}{63}

Apply trig inverse properties

\frac{π}{6} x = arccos (\frac{140 T - 383}{63}) + 2 πn, \frac{π}{6} x = - arccos (\frac{140 T - 383}{63}) + 2 πn

Solve

\frac{π}{6} x = arccos (\frac{140 T - 383}{63}) + 2 πn : x = \frac{6 arccos ( \frac{140 T - 383}{63} )}{π} + 12 n

Solve

\frac{π}{6} x = - arccos (\frac{140 T - 383}{63}) + 2 πn : x = - \frac{6 arccos ( \frac{140 T - 383}{63} )}{π} + 12 n

x = \frac{6 arccos ( \frac{140 T - 383}{63} )}{π} + 12 n, x = - \frac{6 arccos ( \frac{140 T - 383}{63} )}{π} + 12 n

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