What is the general solution for cos(pi/2-x)= 4/5 ?

The general solution for cos(pi/2-x)= 4/5 is x=-2pin+pi/2-0.64350…,x=-2pi-2pin+pi/2+0.64350…

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cos(pi/2-x)= 4/5

cos (\frac{π}{2} - x) = \frac{4}{5}

x = - 2 πn + \frac{π}{2} - 0.64350 \dots, x = - 2 π - 2 πn + \frac{π}{2} + 0.64350 \dots

Solution steps

cos (\frac{π}{2} - x) = \frac{4}{5}

Apply trig inverse properties

\frac{π}{2} - x = arccos (\frac{4}{5}) + 2 πn, \frac{π}{2} - x = 2 π - arccos (\frac{4}{5}) + 2 πn

Solve

\frac{π}{2} - x = arccos (\frac{4}{5}) + 2 πn : x = - 2 πn + \frac{π}{2} - arccos (\frac{4}{5})

Solve

\frac{π}{2} - x = 2 π - arccos (\frac{4}{5}) + 2 πn : x = - 2 π - 2 πn + \frac{π}{2} + arccos (\frac{4}{5})

x = - 2 πn + \frac{π}{2} - arccos (\frac{4}{5}), x = - 2 π - 2 πn + \frac{π}{2} + arccos (\frac{4}{5})

Show solutions in decimal form

x = - 2 πn + \frac{π}{2} - 0.64350 \dots, x = - 2 π - 2 πn + \frac{π}{2} + 0.64350 \dots

6 = 10 cos (4 \cdot o)

2 cos (2 θ) + 5 cos (θ) = 4

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

sin^{2} (θ) - sin (θ) = 2

x, sin (x) cos (x) = 0

What is the general solution for cos(pi/2-x)= 4/5 ?
The general solution for cos(pi/2-x)= 4/5 is x=-2pin+pi/2-0.64350…,x=-2pi-2pin+pi/2+0.64350…