Question

Fill in Sin, Cos, and tan ratio for angle x. Sin X = 4/5 (28/35 simplified)

Answer 1

Answer:

Given: $\sin(x) = (4/5)$.

Assuming that $0 < x < 90^{\circ}$, $\cos(x) = (3/5)$ while $\tan(x) = (4/3)$.

Step-by-step explanation:

By the Pythagorean identity $\sin^{2}(x) + \cos^{2}(x) = 1$.

Assuming that $0 < x < 90^{\circ}$, $0 < \cos(x) < 1$.

Rearrange the Pythagorean identity to find an expression for $\cos(x)$.

$\cos^{2}(x) = 1 - \sin^{2}(x)$.

Given that $0 < \cos(x) < 1$:

$\begin{aligned} &\cos(x) \\ &= \sqrt{1 - \sin^{2}(x)} \\ &= \sqrt{1 - \left(\frac{4}{5}\right)^{2}} \\ &= \sqrt{1 - \frac{16}{25}} \\ &= \frac{3}{5}\end{aligned}$.

Hence, $\tan(x)$ would be:

$\begin{aligned}& \tan(x) \\ &= \frac{\sin(x)}{\cos(x)} \\ &= \frac{(4/5)}{(3/5)} \\ &= \frac{4}{3}\end{aligned}$.