Question

if cot theta = -4/3 and theta lies between π/2 and π find the values of sin theta and cos theta​

Answer 1

Answer:

$sin$Ф = 3/5

 cos Ф = -4/5

Step-by-step explanation:

cotФ = -4/3

or  cos Ф/sinФ = -4/3

or cosФ =$\frac{-4}{3}$ sinФ ..........(i)

Now, we know that $cos^{2}$Ф + $sin^{2}$Ф = 1

using (i) , we get-

$\frac{16}{9}sin^2$Ф + $sin^2$Ф = 1

or  $sin^2$Ф = 9/25

or $sin$Ф = ±$\frac{3}{5}$

since, π/2 <Ф<π

Therefore,

$sin$Ф = 3/5

and  cos Ф = -4/5

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