Question

question 1
the terminal side of an angle in standard position passes through the given point. find the quadrant angle terminates and the exact values of the three trig functions of .
(-5,12)
quadrant sinθ secθ cotθ
type in 1, 2, 3 or 4 for the quadrant. for the trig ratios, type in the fraction and make sure the negative is at the beginning of the fraction if necessary. examples: 1/2 or -1/2 these examples are not the answer.

Explanation:

Step1: Determine the quadrant

The point (-5, 12) has a negative x - coordinate and a positive y - coordinate. Points with x<0 and y > 0 lie in the second quadrant.

Step2: Calculate the radius r

Use the formula $r=\sqrt{x^{2}+y^{2}}$, where $x=-5$ and $y = 12$. So $r=\sqrt{(-5)^{2}+12^{2}}=\sqrt{25 + 144}=\sqrt{169}=13$.

Step3: Find $\sin\theta$

The formula for $\sin\theta=\frac{y}{r}$. Substituting $y = 12$ and $r = 13$, we get $\sin\theta=\frac{12}{13}$.

Step4: Find $\sec\theta$

Since $\sec\theta=\frac{r}{x}$, substituting $r = 13$ and $x=-5$, we get $\sec\theta=-\frac{13}{5}$.

Step5: Find $\cot\theta$

Since $\cot\theta=\frac{x}{y}$, substituting $x=-5$ and $y = 12$, we get $\cot\theta=-\frac{5}{12}$.

Answer:

2
$\frac{12}{13}$
$-\frac{13}{5}$
$-\frac{5}{12}$