7.4.3 – Solving Quadratic Like Trig Equations, Application

Recall, 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 equations

Solving Quadratics Methods to solve algebraic quadratics: – 1) Factor – 2) Quadratic Equation – 3) Graph, approximate In the case of trig, we can really only use options 1 and 3

Key Tip It’s hard to factor at times when you have cos, sin or other trig functions floating around Look to replace those terms with “x” or a standard variable Treat as an algebraic expression; replace trig functions when necessary

Example. Solve the quadratic like equation 2sin 2 x – sinx – 1 = 0

Example. Solve the equation tan 2 x + 2tanx = 3

Example. Solve the equation 2cos 2 x - √3cosx = 0

Application When an object is shot in the air according to the angle θ, we can determine the range of the object traveled by the equation: r = (1/32) v 2 0 sin(2θ) – V 0 = 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 θ from the range using the previous equation.

Assignment Pg , 85