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If cos theta = -2/3, which of the following are possible?

A. csc theta = 3/root5 and tan theta = -root5/2
B. sin theta = -root5/3 and tan theta = root5/2
C. sin theta = root5/3 and tan theta = root5/2
D. csc theta = -3/2 and tan that root 5/2

1 Answer

3 votes

Answer:

B.
\sin \theta=(-√(5))/(3) and
\tan \theta =(√(5))/(2)

Explanation:

We are given that,


\cos \theta=(-2)/(3).

Since, we know,


\sin^2 \theta+\cos^2 \theta=1

i.e.
\sin^2 \theta=1-\cos^2 \theta

i.e.
\sin^2 \theta=1-((-2)/(3))^2

i.e.
\sin^2 \theta=1-(4)/(9)

i.e.
\sin^2 \theta=(9-4)/(9)

i.e.
\sin^2 \theta=(5)/(9)

i.e.
\sin \theta=\pm (√(5))/(3)

Also, we get,


\tan \theta =(\sin \theta)/(\cos \theta)

i.e.
\tan \theta =(\pm (√(5))/(3))/((-2)/(3))

i.e.
\tan \theta =\mp (√(5))/(2)

So, we get that,

Option B is correct.

User GetShifting
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