Question

If sin⁡ θ=−4/5, and 270° < θ < 360°what is cos θ?

Answer 1

Here is your answer

$[I am using ☆ instead of theta]$

$sin☆= -4/5$

${sin}^{2}☆= {(-4/5)}^{2}= 16/25$

Now,

$cos☆= \sqrt{1-{sin}^{2}☆}$

$cos☆= \sqrt{1- (16/25)}$

$cos☆= \sqrt{(25-16)/25}$

$cos☆= \sqrt{9/25}$

$cos☆= 3/5$

HOPE IT IS USEFUL

Answer 2

Answer:

cosΘ = $\frac{3}{5}$

Step-by-step explanation:

Using the trigonometric identity

sin² x + cos²x = 1

⇒ cosx = ± $\sqrt{1-sin^2x}$

Since 270 < Θ < 360 then cosΘ > 0

cosΘ = $\sqrt{1-(4/5)^2}$

         = $\sqrt{1-\frac{16}{25} }$

         = $\sqrt{\frac{9}{25} }$ = $\frac{3}{5}$