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5.3 Solving Trigonometric EquationsSolving trigonometric equations is similar to solving algebraic equations in that you may need to:- isolate the trig function (like isolating the variable)- combine like terms- factor and set factors equal to zero- square both sides of the equation- use the quadratic formula if necessaryWhen solving a trig equation, in addition to the typical strategies listed above for algebraic equations, ask yourself these basic questions...1. Are the trig functions the same?2. Are the angles the same or multiples of each other?3. What is the domain? Is it a given interval or all real numbers?How you proceed to solve the equation depends on the three critical questions above. In addition to solving trig equations algebraically, you can solve them on your graphing calculator. Use your graphing calculator to CHECK the solutions for each example below after solving algebraically. Day 1:CASE 1. Are the trig functions the same?(HINT: Isolate the trig function.)(HINT: Use a trig identity to make a substitution.)YES. Only one trig function in the equation.NO. More than one trig function in the equation.2sinx−3=00≤x<2π23302sincosxx+−=0≤x<2π
sinx+cosx⋅cotx=20≤x<2πtan3x=3tanx[0,2π)Day 2:CASE 2. Is the angle “x” or a multiple of “x” (like 2x, 3x, x/2, etc)? (HINT: If the equation contains a multiple angle 2x, 3x, etc. remember to adjust the domain.)1.) 2310cost−=0≤t<2π2.) 4sin22x=30≤x<2π3.) tan2x(tanx−1)0≤x<2π4.) tanx2=−130≤x<2π(HOMEWORK HINT:In homework – do #69 in radians and #73 in degrees)
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