2. Solving Trigonometric Equations Using Inverses
Sign In
The x-intercepts of the graph of a function occur when y=0.
32π+2πn radians, 34π+2πn radians, for any integer n
LHS−1=RHS−1
LHS/2=RHS/2
Put minus sign in front of fraction
Rearrange equation
The cosine of an angle in standard position is the x-coordinate of the point of intersection of the unit circle and the terminal side of the angle. The solution θ=32π is in Quadrant II, so the second solution must be in Quadrant III. Because these angles are symmetric across the x-axis and a full turn measures 2π radians, to find this angle we subtract 32π from 2π.