Solving Trigonometric Equations

When solving trig equations, this is NOT quite the way to do it:

Ex. Solve each equation for ALL values of x. 1. We have solved a lot of types of equations… utilize the knowledge and methods that we have already used in solve trig equations. This is a ‘quadratic-type’ equation… …so let u=sinx (not possible since sin x must be≤1) Factor: prod=ac=4 sum=b=-5 -1, -4 -5 There are MANY angles that have sinx=1/2. 30˚ & any number of rotations that ‘land’ on 30˚…which means 30˚+360k˚ and 150˚ and any number of rotations that ‘land’ on 150˚…which means 150˚+360k˚ where k is the number of rotations. Rewrite: Group: Factor: x= 30˚+360k˚ & 150˚+360k˚ Subst:

Ex. Solve each equation for ALL values of x. 2. or x = -45˚+180k˚(-45˚=315˚)) x = 60˚+360k˚ or -60˚+360k˚ (-60˚=300˚) This time it’s 180k˚ because tangents have same sign in Quads. II & IV.

Ex. Solve each equation for 0≤x≤180˚. 3. 4. or x = 0˚or 180˚ or 30˚or 150˚ x = 45˚or 135˚