Question

Let θ be an angle in quadrant 2 such that cos(θ)=-5/13. Find the exact values of cscθ and tanθ.

Answer 1

Well find the Opposite, Adjacent and Hypotenuse with the pythagorean theorem

Answer 2

which is one way

Answer 3

you already know the Hypotenuse and the Adjacent since cos = A/H
so, a = -5 and H = 13

Answer 4

\[a^2 + b^2 = c^2\]

Answer 5

\[c^2 - a^2 = b^2\]

Answer 6

so..
\[13^2 - 5^2 = b^2\]

Answer 7

(b is the opposite side)

Answer 8

\[169 - 25 = 144\]

Answer 9

\[\sqrt{144} = 12\]

Answer 10

now you know that the opposite side = 12

Answer 11

so A = -5, H = 13, O = 12

Answer 12

tan = O/A and csc = H/O