What is the general solution for 1/(cos(x))=1.98 ?

The general solution for 1/(cos(x))=1.98 is x=1.04135…+2pin,x=2pi-1.04135…+2pin

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1/(cos(x))=1.98

\frac{1}{cos ( x )} = 1.98

x = 1.04135 \dots + 2 πn, x = 2 π - 1.04135 \dots + 2 πn

Solution steps

\frac{1}{cos ( x )} = 1.98

Multiply both sides by

cos (x)

1 = 1.98 cos (x)

Switch sides

1.98 cos (x) = 1

Multiply both sides by

100

198 cos (x) = 100

Divide both sides by

198

cos (x) = \frac{50}{99}

Verify Solutions

Find undefined (singularity) points:

cos (x) = 0

Combine undefined points with solutions:

cos (x) = \frac{50}{99}

Apply trig inverse properties

x = arccos (\frac{50}{99}) + 2 πn, x = 2 π - arccos (\frac{50}{99}) + 2 πn

Show solutions in decimal form

x = 1.04135 \dots + 2 πn, x = 2 π - 1.04135 \dots + 2 πn

2 sin^{2} (3 θ) - 1 = 0

4 sin (4 θ - \frac{π}{3}) + 3 = 5

2 tan (x) - 3 = 0

- 2 cos (2 x - \frac{π}{3}) = 2 sin (2 x - \frac{π}{6})

tan (x) = 5 sin (\frac{π}{4}) sin (\frac{3 π}{4})

What is the general solution for 1/(cos(x))=1.98 ?
The general solution for 1/(cos(x))=1.98 is x=1.04135…+2pin,x=2pi-1.04135…+2pin