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Home > PC > Chapter 6 > Lesson 6.1.3 > Problem 6-41


Many times when we are solving trigonometric equations, the solutions are not convenient values on the unit circle where we can find the exact answers. For example, when we solve , we get and we know the exact solution between  and is . The other solution between and is . But what happens when we try to solve ?

  1. Solve for and calculate a decimal approximation.

  2. Is this the only solution between and ? Use what you know about the symmetry of the sine wave to determine the other solution between and to this trigonometric equation.

    Use the unit circle and symmetry.

    Where else is the ?

    How can you write this?

    Circle, horizontal & vertical diameter, label at left end of horizontal diameter is pi, label at right end of horizontal diameter is 0, point in first quadrant, about 1 fourth of way from positive y axis, right triangle with hypotenuse from origin to point, horizontal leg on positive x axis.

  3. Using the same method, find all of the solutions for the domain .

    Add where any integer to both answers above.