Question

How do you figure out the csc and sec? For a standard-position angle determined by the point (x, y), what are the values of the trigonometric functions?
For the point (9, 12), find csc theta and sec theta

Answer 1

Answer:

$cosec{\theta}=\frac{15}{12}$ and $sec{\theta}=\frac{15}{9}$

Step-by-step explanation:

For the standard position triangle having sides of x=9 and y=12 and the included theta, the hypotenuse can be calculated through the Pythagorean theorem such as:

$(AC)^2=(AB)^2+(BC)^2$

$(AC)^2=144+81$

$(AC)^2=225$

$AC=15$

Therefore, the value of AC(Hypotenuse) is 13 units.

Now, $cosec{\theta}=\frac{AC}{AB}$

$cosec{\theta}=\frac{15}{12}$

and $sec{\theta}=\frac{AC}{BC}$

$sec{\theta}=\frac{15}{9}$

which are the required values of $cosec{\theta}$ and $sec{\theta}$.

Answer 2

choices....
a. csc = 15/12 sec = 15/9
b. csc = 15/12 sec = 12/15
c. csc = 9/15 sec = 12/15
d. csc = 9/12 sec = 9/15

a = 9 ; b = 12 ; c = ?

Pythagorean theorem: a² + b² = c²
9² + 12² = c²
81 + 144 = c²
225 = c²
√225 = √c²
15 = c

CSC = cosecant function = hypotenuse/opposite = 15/12 
SEC = secant function = hypotenuse/adjacent = 15/9

Choice A: csc = 15/12 sec = 15/9