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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

Respuesta :

taskmasters
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 

boffeemadrid

Answer:

[tex]cosec{\theta}=\frac{15}{12}[/tex] and [tex]sec{\theta}=\frac{15}{9}[/tex]

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:

[tex](AC)^2=(AB)^2+(BC)^2[/tex]

[tex](AC)^2=144+81[/tex]

[tex](AC)^2=225[/tex]

[tex]AC=15[/tex]

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

Now, [tex]cosec{\theta}=\frac{AC}{AB}[/tex]

[tex]cosec{\theta}=\frac{15}{12}[/tex]

and [tex]sec{\theta}=\frac{AC}{BC}[/tex]

[tex]sec{\theta}=\frac{15}{9}[/tex]

which are the required values of [tex]cosec{\theta}[/tex] and [tex]sec{\theta}[/tex].

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