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Popular Trigonometry >

0.428=cos(1.57*x-pi)

Solution

0.428 = cos (1.57 \cdot x - π)

Solution

x = \frac{1.12851 \dots}{1.57} + \frac{2 πn}{1.57} + \frac{π}{1.57}, x = \frac{3 π}{1.57} + \frac{2 πn}{1.57} - \frac{1.12851 \dots}{1.57}

+1

Degrees

x = 155.83394 \dots^{\circ} + 229.29936 \dots^{\circ} n, x = 302.76477 \dots^{\circ} + 229.29936 \dots^{\circ} n

Solution steps

0.428 = cos (1.57 x - π)

Switch sides

cos (1.57 x - π) = 0.428

Apply trig inverse properties

cos (1.57 x - π) = 0.428

General solutions for

cos (1.57 x - π) = 0.428

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

1.57 x - π = arccos (0.428) + 2 πn, 1.57 x - π = 2 π - arccos (0.428) + 2 πn

1.57 x - π = arccos (0.428) + 2 πn, 1.57 x - π = 2 π - arccos (0.428) + 2 πn

Solve

1.57 x - π = arccos (0.428) + 2 πn : x = \frac{arccos ( 0.428 )}{1.57} + \frac{2 πn}{1.57} + \frac{π}{1.57}

1.57 x - π = arccos (0.428) + 2 πn

Move

π

to the right side

1.57 x - π = arccos (0.428) + 2 πn

Add

π

to both sides

1.57 x - π + π = arccos (0.428) + 2 πn + π

Simplify

1.57 x = arccos (0.428) + 2 πn + π

1.57 x = arccos (0.428) + 2 πn + π

Divide both sides by

1.57

1.57 x = arccos (0.428) + 2 πn + π

Divide both sides by

1.57

\frac{1.57 x}{1.57} = \frac{arccos ( 0.428 )}{1.57} + \frac{2 πn}{1.57} + \frac{π}{1.57}

Simplify

x = \frac{arccos ( 0.428 )}{1.57} + \frac{2 πn}{1.57} + \frac{π}{1.57}

x = \frac{arccos ( 0.428 )}{1.57} + \frac{2 πn}{1.57} + \frac{π}{1.57}

Solve

1.57 x - π = 2 π - arccos (0.428) + 2 πn : x = \frac{3 π}{1.57} + \frac{2 πn}{1.57} - \frac{arccos ( 0.428 )}{1.57}

1.57 x - π = 2 π - arccos (0.428) + 2 πn

Move

π

to the right side

1.57 x - π = 2 π - arccos (0.428) + 2 πn

Add

π

to both sides

1.57 x - π + π = 2 π - arccos (0.428) + 2 πn + π

Simplify

1.57 x = 3 π + 2 πn - arccos (0.428)

1.57 x = 3 π + 2 πn - arccos (0.428)

Divide both sides by

1.57

1.57 x = 3 π + 2 πn - arccos (0.428)

Divide both sides by

1.57

\frac{1.57 x}{1.57} = \frac{3 π}{1.57} + \frac{2 πn}{1.57} - \frac{arccos ( 0.428 )}{1.57}

Simplify

x = \frac{3 π}{1.57} + \frac{2 πn}{1.57} - \frac{arccos ( 0.428 )}{1.57}

x = \frac{3 π}{1.57} + \frac{2 πn}{1.57} - \frac{arccos ( 0.428 )}{1.57}

x = \frac{arccos ( 0.428 )}{1.57} + \frac{2 πn}{1.57} + \frac{π}{1.57}, x = \frac{3 π}{1.57} + \frac{2 πn}{1.57} - \frac{arccos ( 0.428 )}{1.57}

Show solutions in decimal form

x = \frac{1.12851 \dots}{1.57} + \frac{2 πn}{1.57} + \frac{π}{1.57}, x = \frac{3 π}{1.57} + \frac{2 πn}{1.57} - \frac{1.12851 \dots}{1.57}

Graph

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