Problem: Solve: 5 Sin x + 2 = 0; x [0,2π]
Solution First, solve for Cos x.
Solution 5Sin x + 2 = 0
Step 2: 5Sin x = -2
Sin x = -2/5
Solution Now, Sine is negative in Quadrant III and Quadrant IV.
Step 3: Also, a sine value of 2/5 is a reference angle of 23.6º.So;
consider the reference angle of 23.6º in quadrants III and IV.
x = 118.4° and 165.8° or 5π/7.6 and 7π/7.6
Solution Answer: x = 118.4° and 165.8°
Try two practice problems:
Solve the following: