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7.4.3 – Solving Quadratic Like Trig Equations, Application

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)

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7.4.3 – Solving Quadratic Like Trig Equations, Application

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  1. 7.4.3 – Solving Quadratic Like Trig Equations, Application

  2. 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

  3. 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

  4. 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

  5. Example. Solve the quadratic like equation 2sin2x – sinx – 1 = 0

  6. Example. Solve the equation tan2x + 2tanx = 3

  7. Example. Solve the equation 2cos2x - √3cosx = 0

  8. 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) v20 sin(2θ) • V0 = initial velocity

  9. 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.

  10. Assignment • Pg. 587 • 59-65, 85

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