Given cosΘ=2/3 and sinΘ>0, find sinΘ (Just for clarification, those zeros with horizontal lines in the center represent theta

Question

Given cosΘ=2/3 and sinΘ>0, find sinΘ

(Just for clarification, those zeros with horizontal lines in the center represent theta)

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Doris 3 months 2021-08-09T12:02:41+00:00 1 Answers 2 views 0

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    2021-08-09T12:03:57+00:00

    Answer:

    sinΘ = √5/3

    Step-by-step explanation:

    Mathematically, we know that the cos of an angle is the ratio of the adjacent to the hypotenuse

    The sine of an angle is the ratio of the opposite to the hypotenuse

    So in this case, from the cosine given; adjacent is 2 and hypotenuse is 3

    From the Pythagoras’ theorem, we can get the opposite

    Mathematically, the square of the hypotenuse equals the sum of the squares of the two other sides

    Let us have the opposite as x

    3^2 = 2^2 + x^2

    9 = 4 + x^2

    x^2 = 9-4

    x^2 = 5

    x = √5

    This root can be positive or negative

    But since the sine is positive, we shall be considering only the positive root

    Thus;

    sine theta = √5/3

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