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

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

Answer Link

boffeemadrid boffeemadrid · Answer 2 · 2019-05-22T05:50:30-04:00

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 \(sec{\theta}\).

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

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Related Questions

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