Question

test 5 - chapter 5
score: 13/14 answered: 13/14
question 13
given that the point (-108, 45) is on the terminal side of an angle, θ, find the exact value of the following:
sin(θ)=
cos(θ)=
tan(θ)=
csc(θ)=
sec(θ)=
cot(θ)=

Explanation:

Step1: Calculate radius r

$r=\sqrt{(- 108)^2 + 45^2}=\sqrt{11664 + 2025}=\sqrt{13689}=117$

Step2: Find sin(θ)

$\sin(\theta)=\frac{y}{r}=\frac{45}{117}=\frac{5}{13}$

Step3: Find cos(θ)

$\cos(\theta)=\frac{x}{r}=\frac{-108}{117}=-\frac{12}{13}$

Step4: Find tan(θ)

$\tan(\theta)=\frac{y}{x}=\frac{45}{-108}=-\frac{5}{12}$

Step5: Find csc(θ)

$\csc(\theta)=\frac{r}{y}=\frac{117}{45}=\frac{13}{5}$

Step6: Find sec(θ)

$\sec(\theta)=\frac{r}{x}=-\frac{117}{108}=-\frac{13}{12}$

Step7: Find cot(θ)

$\cot(\theta)=\frac{x}{y}=-\frac{108}{45}=-\frac{12}{5}$

Answer:

$\sin(\theta)=\frac{5}{13}$
$\cos(\theta)=-\frac{12}{13}$
$\tan(\theta)=-\frac{5}{12}$
$\csc(\theta)=\frac{13}{5}$
$\sec(\theta)=-\frac{13}{12}$
$\cot(\theta)=-\frac{12}{5}$