I need help with these kind of problems!

Can someone tell me how to work this problem out?
Given tan0=2 square root of 5 over 4, and sin0<0.
a. cos0 b. csc0
The 0 after tan, sin, cos, and csc stands for angle. The 0 after the < stands for negative or less than. I know it sounds confusing, but if somebody knows a great web site to get help from, please inform me!

To find the values of cos0 and csc0 given the information provided, we can use the trigonometric identity:

sin^2θ + cos^2θ = 1

Given that sin0 < 0, we know that the angle is in the third or fourth quadrant, where cosine is negative.

Step 1: Find sin0
We're given that tan0 = 2√5/4. We can use the fact that tanθ = sinθ/cosθ:

tan0 = sin0/cos0

sin0 = tan0 * cos0

We know that tan0 = 2√5/4, so:

sin0 = (2√5/4) * cos0

Step 2: Solve for cos0
Using the Pythagorean identity mentioned earlier:

sin^2θ + cos^2θ = 1

(sin0)^2 + (cos0)^2 = 1

Substituting the value of sin0 obtained in Step 1:

[(2√5/4) * cos0]^2 + (cos0)^2 = 1

(4√5/4 * cos0)^2 + (cos0)^2 = 1

Simplifying:

(20/16) * (cos0)^2 + (cos0)^2 = 1

(20/16 + 1) * (cos0)^2 = 1

20/16 + 1 = 36/16

(36/16) * (cos0)^2 = 1

(9/4) * (cos0)^2 = 1

(cos0)^2 = 4/9

Taking the square root of both sides:

cos0 = ± √(4/9)

Since cos0 is negative in the third and fourth quadrants:

cos0 = -√(4/9) = -2/3

So the answer to part a is cos0 = -2/3.

Step 3: Solve for csc0
Using the identity cscθ = 1/sinθ:

csc0 = 1/sin0

We obtained the value of sin0 in Step 1:

csc0 = 1/[(2√5/4) * cos0]

Simplifying:

csc0 = 4 / [2√5 * cos0]

csc0 = 2 / (√5 * cos0)

Substituting the value of cos0 obtained in Step 2:

csc0 = 2 / (√5 * (-2/3))

Simplifying:

csc0 = -6 / (2√5)

csc0 = -3 / √5

To rationalize the denominator, we can multiply both the numerator and denominator by √5:

csc0 = (-3/√5) * (√5/√5)

csc0 = -3√5 / 5

So the answer to part b is csc0 = -3√5 / 5.