Question

Assume that θ is an angle in standard position whose terminal side contains the point (5, -12). Find the exact value of the following functions.

Answer 1

Step-by-step explanation

The relation between polar and cartesian coordinates is given by:

In this case, we have:

`P(x,y)=P(5,-12)\Rightarrow r={√(x^2+y^2)}=√(5^2+(-12)^2)=√(169)=13.`Answer

Using the formulas above and the values of x, y and r, we have:

1) sin θ

`\sinθ=(y)/(r)=-(12)/(13).`

2) cos θ

`\cosθ=(x)/(r)=(5)/(13).`

3) tan θ

`\tanθ=(y)/(x)=-(12)/(5).`

4) csc θ

`csc\text{ }\theta=\frac{1}{sin\text{ }\theta}=(1)/((-(12)/(13)))=-(13)/(12).`

5) sec θ

`sec\text{ }\theta=\frac{1}{cos\text{ }\theta}=(1)/((5)/(13))=(13)/(5).`

6) cot θ

`cot\text{ }\theta=(1)/(\tan\theta)=(1)/((-(12)/(5)))=-(5)/(12).`