Question

if sin theta equal to 4/5 and theta is not in the first quadrant find the value if cos theta​

Answer 1

here is the answer of your question

Answer 2

Answer:

The value of  $\bold{cos\theta=-\frac{3}{5} }$

Step-by-step explanation:

Given that $sin\theta=\frac{4}{5}$ and $\theta$ is not in the first quadrant.

As we see that $sin\theta$ is positive so  $\theta$ is the second quadrant.

Now according to Pythagoras theorem:

$AB^{2} +BC^{2} =AC^{2} \\4^{2} +x^{2} =5^2\\16+x^2=25\\x^2=25-16$

Further solving,

$x^2=9\\x=3$

So, $cos\theta=\frac{3}{5}$

As we know that  $\theta$ is in the second quadrant.

$\bold{cos\theta=-\frac{3}{5} }$