Solving trigonometric equations
                        Solving trigonometric equations   1 / 11
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                5π/3
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                x0 = π/3 works.
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                Step 2: Remember that cos(x) = cos(2π−x). What is another solution?
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                x1 = 2π −π/3 =          works.
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                Step 3:Use that cos(x) = cos(x +2πk) for all integers k to get more
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                solutions: x = π/3 + 2πk or x = 5π/3+2πk for any integer k.
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 Can you think of an angle with cos(x) = 1/2. Look at your unit circles if
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 you must.
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 For you: Find all the solutions to sin(x) = 1/2.
  A strategy for solving equations involving trig functions.
   Let’s recall how to solve cos(x) = 1/2.
   Step one: Get a preliminary solution.
                                Solving trigonometric equations             2 / 11
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  5π/3
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 x0 = π/3 works.
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 Step 2: Remember that cos(x) = cos(2π−x). What is another solution?
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 x1 = 2π −π/3 =          works.
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 Step 3:Use that cos(x) = cos(x +2πk) for all integers k to get more
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 solutions: x = π/3 + 2πk or x = 5π/3+2πk for any integer k.
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 For you: Find all the solutions to sin(x) = 1/2.
  A strategy for solving equations involving trig functions.
   Let’s recall how to solve cos(x) = 1/2.
   Step one: Get a preliminary solution.
   Can you think of an angle with cos(x) = 1/2. Look at your unit circles if
   you must.
                                Solving trigonometric equations             2 / 11
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  5π/3
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 Step 2: Remember that cos(x) = cos(2π−x). What is another solution?
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 x1 = 2π −π/3 =          works.
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 Step 3:Use that cos(x) = cos(x +2πk) for all integers k to get more
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 solutions: x = π/3 + 2πk or x = 5π/3+2πk for any integer k.
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 For you: Find all the solutions to sin(x) = 1/2.
  A strategy for solving equations involving trig functions.
   Let’s recall how to solve cos(x) = 1/2.
   Step one: Get a preliminary solution.
   Can you think of an angle with cos(x) = 1/2. Look at your unit circles if
   you must.
   x =π/3 works.
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                                Solving trigonometric equations             2 / 11