turkey-yks 2018 Q29

turkey-yks · Other · yks-ayt Trig Proofs Trigonometric Identity Simplification
Below are shown a semicircle with center O and radius 1 unit, and right triangles OAB and ODC. Points A and C lie on both the triangle OAB and the semicircle.
Accordingly, $$\frac { | \mathrm { AB } | + | \mathrm { BC } | } { | \mathrm { CD } | + | \mathrm { DA } | }$$
What is the equivalent of this ratio in terms of x?
A) $\sin x$ B) $\tan x$ C) $\cot x$ D) $\csc x$ E) $\sec x$
Below are shown a semicircle with center O and radius 1 unit, and right triangles OAB and ODC. Points A and C lie on both the triangle OAB and the semicircle.

Accordingly,
$$\frac { | \mathrm { AB } | + | \mathrm { BC } | } { | \mathrm { CD } | + | \mathrm { DA } | }$$

What is the equivalent of this ratio in terms of x?

A) $\sin x$
B) $\tan x$
C) $\cot x$
D) $\csc x$
E) $\sec x$