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kobusy [5.1K]
3 years ago
10

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

Mathematics
2 answers:
Sergeeva-Olga [200]3 years ago
8 0
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
PilotLPTM [1.2K]3 years ago
6 0

Answer: - sqrt 5 / 3

Step-by-step explanation:

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