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Warm UP!

Warm UP!. Solve 2 sin 2  + 3 sin  + 1 = 0 for [0,360]. y=sin x. y. 1. y =. x. 180. 360. 540. -180. -360. -540. 720. -1. Solving Graphically. sin x = is a trigonometric equation. x = 30 is one of infinitely many solutions of y = sin x.

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Warm UP!

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  1. Warm UP! Solve 2 sin2 + 3 sin  + 1 = 0 for [0,360]

  2. y=sin x y 1 y = x 180 360 540 -180 -360 -540 720 -1 Solving Graphically sin x = is a trigonometric equation. x = 30 is one of infinitely many solutions of y = sin x. All the solutions for x can be expressed in the form of a general solution. x = 30 + 360k and x = 150+ 360k (k = 0, ±1, ± 2, ± 3,  ).

  3. Solving Trig Equations • What if you are asked to solve cos(x) = 0.75? • 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

  4. Solve sin(x)= cos(x). • What this really means is: “Find the intersection points of the graphs of • y = sin(x) and y = cos(x)” • Type both equations into your calculator now.

  5. 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].

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

  7. 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]?

  8. What are the solutions to 5sin(2x – 30) = cos(x) + 1 on [0,360]? • What are the solutions to tan(x) – 2 – cos(2x) on [-90,270]?

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