HELP PLS//// Suppose that cos0=4/9 and that 3π/2 <0 <2π. Find the values of sin0, tan0, csc0, sec0, and cot0.

Question

sin0=?

tan0=?

csc0=?

sec0=?

cot0=?

Answer 1

Between 3π/2 and 2π (quadrant 4), a sketch would look like this:

because cos(θ) = adjacent/hypotenuse meaning we can draw the adjacent side as "4" units long and the hypotenuse as "9" units long. To find the other side of the triangle, use the Pythagorean Theorem:

4² + y² = 9²

16 + y² = 81

y² = 81 - 16

y² = 65

y = √65

Now we can write the 6 trig functions:

cos(θ) = 4/9

sin(θ) = opp/hyp = √65/9

tan(θ) = opp/adj = √65/4

etc