Question

If cos(0)=5/17, find sin(0) and tan(0) in quadrant 4.

a) sin(0)= −12/17, tan(0)=12/5
b) sin(0)= −5/12, tan(0)= 5/12
c) sin(0)= −12/5, tan(0)= 5/12
d) sin(0)= −5/17, tan(0)= 5/17

Answer 1

In Quadrant 4, sin(0) is -12/17 and tan(0) is -12/5.

Step-by-step explanation:

To find sin(0) and tan(0) in Quadrant 4, we can use the trigonometric identities and the given information that cos(0) = 5/17.

First, let's find sin(0) using the Pythagorean identity, which states that sin^2(theta) + cos^2(theta) = 1.

Since we are in Quadrant 4 and cos(0) = 5/17, we know that sin(0) is negative. Therefore, sin(0) = -sqrt(1 - cos^2(0)) = -12/17.

Next, we can use the definition of tan(0) = sin(0)/cos(0). Plugging in the values, we get tan(0) = (-12/17) / (5/17) = -12/5.