Question

(6,-5) is a point on the terminal side of 0. Find the exact values of cos0, csc0, and tan0.

Answer 1

Answer:

Solutions given:

(6,-5)=(x,y)

r=$\sqrt{6²+(-5)²}=\sqrt{61}$

Now

Sin θ=$\frac{y}{r}$=$\frac{-5}{\sqrt{61}}$

Cosθ=$\frac{x}{r}$=$\frac{6}{\sqrt{61}}$

CSC θ=$\frac{r}{y}$=$\frac{\sqrt{61}}{-5}$

Tan θ=θ=$\frac{y}{x}$=$\frac{-5}{6}$

Note:

p=y

b=x

h=r

Answer 2

point (6, -5) => x = 6, y = -5

r =√6² +(-5)² = √(36+25)=√61

the exact value of :

cos 0 = x/r = 6/√61 = 6/61 √61

csc 0 = r/y = √61/(-5) = -1/5 √61

tan 0 = y/x = -5/6