Question

Suppose cos(A) = 4/5 Use the trig identity sin^2 (A) + cos^2 (A)= 1 to find sin(A) in quadrant IV. Round to ten-thousandth.-0.39540.64850.4500-0.6000

Answer 1

Given:

$cos\left(A\right)=\frac{4}{5}$

To find: The angle A lies in the fourth quadrant.

$sinA$

Explanation:

Using the trigonometric identity,

$\begin{gathered} sin^2A+cos^2A=1 \\ sin^2A+(\frac{4}{5})^2=1 \\ sin^2A+\frac{16}{25}=1 \\ sin^2A=1-\frac{16}{25} \\ sin^2A=\frac{9}{25} \\ sinA=\pm\sqrt{\frac{9}{25}} \\ sinA=\pm\frac{3}{5} \end{gathered}$

Since the angle lies in the fourth quadrant.

So, the sine value in the fourth quadrant will be negative,

$\begin{gathered} sinA=-\frac{3}{5} \\ sinA=-0.6000 \end{gathered}$

Final answer:

The value of sine of A is,

$sinA=-0.6000$