if sin theta= 2/3 and tan theta<0, what is the value of cos theta

Question

if sin theta= 2/3 and tan theta<0, what is the value of cos theta

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Aaliyah 2 months 2021-10-03T18:49:13+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-10-03T18:50:56+00:00

    Answer: – sqrt 5 / 3

    Step-by-step explanation:

    0
    2021-10-03T18:51:08+00:00

    cos
    θ
    =

    5
    3

    or it could be cos
    θ
    =

    5

    3

    Explanation:
    Since sin
    θ
    is negative, it can be in the third or fourth quadrant
    Drawing your right-angled triangle, place your
    θ
    in one of three corners. Your longest side will be 3 and the side opposite the
    θ
    will be -2. Finally, using Pythagoras theorem, your last side should be

    5

    Now, if your triangle was in the third quadrant, you would have
    cos
    θ
    =

    5

    3
    since cosine is negative in the third quadrant
    But if your triangle was in the fourth quadrant, you would have
    cos
    θ
    =

    5
    3
    since cosine is positive in the fourth quadrant

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