Question

If cos 0 = 3/5
and angle 0 is in Quadrant IV, what is the value of tan 0 ?
Tan =

Answer 1

The value of tan 0, given cos 0 = 3/5 and angle 0 in Quadrant IV, is -4/5.

Step-by-step explanation:

To find the value of tan 0, we can use the trigonometric identity tan² 0 = 1 - cos² 0. Since we know that cos 0 = 3/5, we can substitute this value into the equation:

tan² 0 = 1 - (3/5)²

Simplifying, we get tan² 0 = 16/25. Taking the square root of both sides, we find that tan 0 = ±4/5. However, since the angle 0 is in Quadrant IV, where tan 0 < 0, we can conclude that the value of tan 0 is -4/5.

Answer 2

-4/3.

Step-by-step explanation:

cos O = 3/5

Using Pythagoras to find the length of the side opposite the angle O:

As the cos of O is adjacent/ hypotenuse, Hypotenuse = 5 , adjacent side = 3 so

opposite side. = sqrt(5^2 - 3^2) = sqrt 16

= 4.

Now the tangent is negative in Q IV so

tan O = opposite / adjacent side = -4/3