7.4.3 Solving Quadratic Like Trig Equations, Application

7.4.3 Solving Quadratic Like Trig Equations, ApplicationRecall, we established ways to solve trig equations using a combination of algebra (inverse operations, isolate the variable) and trig functions (inverse trig functions)

On several occasions, we may solve trig equations which are similar to quadratic equationsSolving QuadraticsMethods to solve algebraic quadratics:1) Factor2) Quadratic Equation3) Graph, approximate

In the case of trig, we can really only use options 1 and 3Key TipIts hard to factor at times when you have cos, sin or other trig functions floating aroundLook to replace those terms with x or a standard variableTreat as an algebraic expression; replace trig functions when necessary Example. Solve the quadratic like equation 2sin2x sinx 1 = 0Example. Solve the equation tan2x + 2tanx = 3Example. Solve the equation 2cos2x - 3cosx = 0ApplicationWhen an object is shot in the air according to the angle , we can determine the range of the object traveled by the equation:

r = (1/32) v20 sin(2)V0 = initial velocity Example. If a rock is shot in the air with an initial velocity of 400 feet per second and the rock lands 700 feet from where it was launched, determine the angle from the range using the previous equation. AssignmentPg. 58759-65, 85