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13 August, 19:19

If sin theta is - 4/5. 270 degrees is less than theta and theta is less than 360 degrees. What is tan theta?

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  1. 13 August, 19:25
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    tan theta = - 4/3.

    Step-by-step explanation:

    The inequality means that theta is in the 4th quadrant (between 270 and 360 degrees.

    The angle whose sine is 4/5 is 53.13 degrees.

    So the angle whose sine is - 4/5 is 306.87 degrees.

    The tangent is negative and the triangle formed by the angle in the 4th quadrant has sides 3, - 4 and 5 (by the Pythagoras theorem).

    So tan theta = opposite / adjacent = - 4/3 (answer).
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