3cos^2(x)=2

Solution

3 cos^{2} (x) = 2

x = 0.61547 \dots + 2 πn, x = 2 π - 0.61547 \dots + 2 πn, x = 2.52611 \dots + 2 πn, x = - 2.52611 \dots + 2 πn

Solution steps

3 cos^{2} (x) = 2

Solve by substitution

cos (x) = \frac{2}{3}, cos (x) = - \frac{2}{3}

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

cos (x) = - \frac{2}{3} : x = arccos (- \frac{2}{3}) + 2 πn, x = - arccos (- \frac{2}{3}) + 2 πn

Combine all the solutions

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

Show solutions in decimal form

x = 0.61547 \dots + 2 πn, x = 2 π - 0.61547 \dots + 2 πn, x = 2.52611 \dots + 2 πn, x = - 2.52611 \dots + 2 πn

3 tan (θ) = 2 sin (θ)

sin (x) = - 0.1

189.4 = 100 tan^{2} (4 5^{\circ} + \frac{θ}{2})

csc (θ) = 1 + cot (θ)

cos (2 x) = 0.98