Math

Given angle theta is bigger than 0 and smaller than 360, determine two possible values of theta where each ration would be true.
a) cos theta= 0.6951
b)sin theta= -0.7571

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asked by Emily
  1. Here is basically the simplest way to do these type of questions.
    I will assume you are familiar with the CAST rule and have a calculator.

    1. Use the absolute value of the given constant and use the inverse of the given trig ratio.
    in this case, enter
    2nd cos .6951 and press the = sign.
    you should get 45.9648...
    That is your "angle in standard position" , namely the first quadrant angle.

    2. The cosine is positive in I and IV
    so Ø = 45.965° or 360-45.965= 314.035°

    b)
    enter 2nd sin .7571 and press = to get
    49.21°
    BUT our sine was negative , so Ø had to be in III or IV
    in III Ø = 180+49.21 = 229.21
    in IV Ø = 360-49.21 = 310.79°

    check these answers with your calculator, they work.

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    posted by Reiny

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