3sec^2(θ)-12=5sec(θ)

Solution

3 sec^{2} (θ) - 12 = 5 sec (θ)

θ = 1.23095 \dots + 2 πn, θ = 2 π - 1.23095 \dots + 2 πn, θ = 2.41885 \dots + 2 πn, θ = - 2.41885 \dots + 2 πn

Solution steps

3 sec^{2} (θ) - 12 = 5 sec (θ)

Solve by substitution

sec (θ) = 3, sec (θ) = - \frac{4}{3}

sec (θ) = 3 : θ = arcsec (3) + 2 πn, θ = 2 π - arcsec (3) + 2 πn

sec (θ) = - \frac{4}{3} : θ = arcsec (- \frac{4}{3}) + 2 πn, θ = - arcsec (- \frac{4}{3}) + 2 πn

Combine all the solutions

θ = arcsec (3) + 2 πn, θ = 2 π - arcsec (3) + 2 πn, θ = arcsec (- \frac{4}{3}) + 2 πn, θ = - arcsec (- \frac{4}{3}) + 2 πn

Show solutions in decimal form

θ = 1.23095 \dots + 2 πn, θ = 2 π - 1.23095 \dots + 2 πn, θ = 2.41885 \dots + 2 πn, θ = - 2.41885 \dots + 2 πn

3 cos (x) - 3 = cos (x)

sin (x) - 1 = - cos (x)

36 cos (2 x) = 0

2 sin^{2} (θ) + sin (θ) = 0, 0 \leq θ < 2 π

sin (x) + cos (x) = 0, - π \leq x \leq π