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12-45.
  1. For each of the following equations, list all of the solutions without using a calculator. Draw a graph or unit circle to support your answers. Then predict the solution that your calculator will give, and use your calculator to check your prediction. Homework Help ✎

    1. 4sin(x) + 2 = 0

    2. 2cos(x) =

    3. tan(x) + 1 = 0

    4. 4cos(x) – 4 = 0

Subtract 2 from both sides and divide by 4 to solve for sin(x).

sin (x) = 1/2

On a unit circle, find the two different times sin(x) = 1/2. To give all of the solutions, remember that every time you go around the circle, that value occurs again. Since there are 2π radians in a circle, add 2πn to each solution.

Use the same method as part (a).

Use the same method as part (a). How is the tangent function different from the sine function?

Remember to check your answers with your calculator!