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Find the exact value of cot theta if csc theta = -4/3 and the terminal side of theta lies in Quadrant III.

Find the exact value of cot theta if csc theta = -4/3 and the terminal side of theta-example-1
User Badmaash
by
6.9k points

1 Answer

3 votes

Answer:

The exact value of cotФ is
(√(7))/(3)

Explanation:

Given as:

The value of cosec Ф =
(-4)/(3)

Let the value of cotФ = x

Now, According to question

sinФ =
(1)/(cosec\Theta ) .....1

Put the value of cosec Ф =
(-4)/(3) in eq 1

i.e sinФ =
(1)/((-4)/(3) )

Or, sinФ =
(-3)/(4)

Again

cosФ =
\sqrt{1-sin^(2)\Theta }

So, cosФ =
\sqrt{1-((-3)/(4))^(2)}

Or, cosФ =
\sqrt{1-((9)/(16))}

Or, cosФ =
\sqrt{(16 - 9)/(16))}

cosФ =
(√(7))/(4)

Again

we know that cotФ =
(cos\Theta )/(sin\Theta )

So, cotФ =
((√(7))/(4))/((-3)/(4))

Or, cotФ =
(-√(7))/(3)

As according to question sinФ lies in third quadrant

So, cotФ =
(√(7))/(3)

Hence, The exact value of cotФ is
(√(7))/(3) . Answer

User Mark Knol
by
6.7k points