Answer:
B and C
Step-by-step explanation:
Right off the top, A and D are both wrong.
A: wrong because the sec is greater than 1. Always
D: C and D cannot be equal to the same thing except when theta = 45 degrees. The right answer is C and therefore D is incorrect.
C: is one of the answers. The CSC(theta) = 1/sin(theta) or Sin(theta) = 1 /CSC(theta) . If that is true, and if CSC(theta) = 13/5 the Sin(theta) = 5/13
The Other correct answer is B. The adjacent side is found from the Pythagorean Theorem
a^2 + b^2 = c^2
a = 5
b = ? and is the adjacent side.
c = 13
5^2 + b^2 = 13^2
25 + b^2 = 169 Subtract 25 from both sides
b^2 = 144 Take the square root of both sides
b = 12
Tan(theta) = 5/12
You may wonder how I knew that 12 was the adjacent side. The reason is because the sin and csc both deal with the opposite side. The tan(theta) needs to know what the adjacent side as well as the opposite side is.
