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

well, If we draw these points on the graph, it would give us a right-angled triangle and then we may apply pythagoras' theorem to get "sin (theta)" & "cos (theta)" and "sec (theta) = 1/cos(theta)" & "csc(theta) = 1/sin(theta)". From the points (as it makes a right-angled triangle), we know
Suppose, a = horizontal side of triangle, b = verticle, and c = longest side (or diagonal)
So, a = 9, b = 12

and applying pythagoras' theorem now, (the theorem is c^2 = a^2 + b^2)
we get
c^2 = 9^2 + 12^2
c^2 = 81 + 144
c^2 = 225
c = 15.
So, now the values of the sides of the triangle are

a = 9, b = 12, c = 15

and, If "theta" is the angle between a & b, then

cos(theta) = 15/12 = 5/4
and, sin(theta) = 15/9 = 5/3

So,

sec(theta) = 1/cos(theta) = 1/(5/4) = 4/5
csc(theta) = 1/sin(theta) = 1/(5/3) = 3/5

That's the answer. HTH :)

Answer 2

Is that the correct answer? can u verify?

Answer 3

I will be able to verify in one minute.

Answer 4

Thats not one of the 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

Answer 5

oh did you mean csc and sec? instead of cos and sin?

Answer 6

yes

Answer 7

Option C is the correct answer