Solving For x in Trigonometric Equations
Solve for x, 0 ≤ x < 2π, sin2x = √2/2 We first change the domain, because it says 2x. That would make 0 ≤ x < 2π into 0 ≤ 2x < 4π, meaning we have to collect answers not once around the unit circle but twice around the unit circle. When sinx = /sqrt2/2, 2x = π/4, 3π/4, 9π/4, 11π/4 Then we solve for x by dividing each answer by 2. x = π/8, 3π/8, 9π/8, 11π/8 Make sure each value is in the original domain 0 ≤ x < 2π
Solve for x, 0 ≤ x < 2π, tan(x/2) = -1 We first change the domain, because it says x/2. That would make 0 ≤ x < 2π into 0 ≤ x/2 < π, meaning we have to collect answers not once around the unit circle but only half around the unit circle. When tanx = -1, x/2 = 3π/4 Then solve for x by multiplying the answer by 2. x = 6π/4 = 3π/2
Solve for x, 0° ≤ x < 360°, cos2x = -0.48 We first change the domain, because it says 2x. That would make 0° ≤ x < 360° into 0° ≤ 2x < 720°, meaning we have to collect answers not once around the unit circle but twice around the unit circle. When cosx = -0.48, 2x = 118.6°, 241.31°, 478.6°, 601.31° Then solve for x by dividing the answers by 2. x = 59.3°, 120.6°, 239.3°, 300.6°
