If , Which Of The Following Represents An Approximate Value Of , For ? 0.7660 0.8392 1.1916 1.4198

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Question

If sin theta = -0.7660, which of the following represents an approximate value of tan theta, for 180 degrees < theta < 270 degrees?

Answer

If sin(theta) = – 0.7660 =>  angle theta = inverse sine of – 0.766.When you plug that into the calculator you get theta  ≈ – 50°.A negative angle means that it is below from the x-axis and that means that the answer of the calculator is 360° – 50° = 310°.As you know that the sine function is negative in third and fourth quadrants you have that the angle theta may be 180° + 50° = 230° and 360° – 50 = 310°.The problem states that the angle is in the third quadrant (180 < theta < 270), so there is only one answer. Theta ≈ 230°.Which you can verifiy when you calculate sine of 230°.Answer: 230°.

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