Question

Evaluate tan(cos^-1 3/5) and assume that all angles are in Quadrant I.

Answer 1

Answer:

Option c

Step-by-step explanation:

We assume that the angle is in the first quadrant.

Observe the attached image.

if $u = cos ^{-1}(\frac{3}{5})$

So:

$cosu = \frac{3}{5}$

By definition:

$cosu= \frac{adjacent}{hypotenuse}$

So:

adjacent side = 3

hypotenuse = 5.

Observe the attached image

We find the opposite side "x" using the Pythagorean theorem.

$x=\sqrt{5^2 -3^2} \\x = 4$

Then, for the angle u:

$tanu = \frac{opposite}{adjacent}\\\\tanu = \frac{x}{3}\\\\tanu = \frac{4}{3}$