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LG 4-1: Solving Trig Equations (TEST 9/27)

Unit 4: Extended Trigonometry. LG 4-1: Solving Trig Equations (TEST 9/27). LG 4-2: Solving Oblique Triangles & Area (TEST 10/02). LG 4-3:Vectors (TEST 10/14). LG 4-1 Solving Trig Equations. MM4A6. Students will solve trigonometric equations both graphically and algebraically.

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LG 4-1: Solving Trig Equations (TEST 9/27)

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  1. Unit 4: Extended Trigonometry LG 4-1: Solving Trig Equations (TEST 9/27) LG 4-2: Solving Oblique Triangles & Area (TEST 10/02) LG 4-3:Vectors (TEST 10/14)

  2. LG 4-1 Solving Trig Equations MM4A6. Students will solve trigonometric equations both graphically and algebraically. • Solve trigonometric equations over a variety of domains, using technology as appropriate. TODAY: You will solve trigonometric equations graphically and algebraically.

  3. Solving Trig Equations • Solve sin(x) = • This is the same as saying “What angle has a sine output of 1?” Sound familiar? • arcsin(1) = 90 • However, there is an infinite number of angles that solve this. Why? • Test one of these coterminal angles now in calculator. • When solving trig equations, you will always be given an interval for your solutions.

  4. PREVIEW Solve

  5. Notes • Follow along with me as we go through all 7 problems. You will finish the problems on the back for classwork/homework!!

  6. Warm UP! • Solve the equation 3sin x + = sin xfor -90 ≤x≤ 90 • Solve sec(x)=2 for [0, 270].

  7. If one value of cos-1(x) = 50o find another value on [0,360] The solution is 310o because this is the only other place where the arccosine would be positive and it is a 50o reference angle. Let’s try some more: 1. If one value of sin-1 = 143o, find another solution on the interval [0,360]. 2. If one value of cos-1 = 125o, find another solution on the interval [0,360].

  8. Think about it… Explain why there are no solutions to sin(x) = 3 but there are solutions to tan(x) = 3.

  9. Graphing Calculator Short Cuts… • How many solutions to sin(3x)+2 = 2cos(x) + 3 are there on [0,180]? • What are the solutions to sin(3x)+2 = 2cos(x) + 3 on [0,180]?

  10. Solving Trig Equations • What if you are asked to solve cos(x) =? • This is different because there are no cosine outputs of 0.75 on the unit circle. • Use your calculator to find the inverse cosine (or arccosine) of 0.75 • If the value you are trying to find is not on the unit circle, you must use your calculator to evaluate (just make sure it is on DEGREE MODE!) • Check your solution using your graphing calculator

  11. Practice • Remember, if you get stuck, you can always try the calculator method. • ALWAYS use the calculator method when asked how many solutions. • ALWAYS use the calculator method when a problem has more than one kind of trig function that can’t be simplified using your booklet.

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