0.428=cos(1.57*x-pi)

Solution

0.428 = cos (1.57 \cdot x - π)

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}

Solution steps

0.428 = cos (1.57 x - π)

Switch sides

cos (1.57 x - π) = 0.428

Apply trig inverse properties

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}

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}

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}

5 = 10 sin (a)

sin (θ) = cos (2 θ + 5 4^{\circ})

t, y = cos (t)

x, r^{2} = 9 cos (2 x)

csc (a) = \frac{13}{12}