Answer
$ a=\sin\theta$
$ b=\tan\theta$
$ c=\sec\theta$
$ d=\cos\theta$
Work Step by Step
From the inner triangle (with legs a and d, 1 as hypotenuse):
a is opposite to $\displaystyle \theta,\quad \sin\theta=\frac{a}{1} \ \Rightarrow \ a=\sin\theta$
d is adjacent to $\displaystyle \theta,\quad \cos\theta=\frac{d}{1} \ \Rightarrow \ d=\cos\theta$
From the outer triangle (legs b and 1, hypotenuse c):
b is opposite, 1 is adjacent to $\theta$,
$\displaystyle \tan\theta=\frac{b}{1} \ \Rightarrow \ b=\tan\theta$
1 is adjacent to $\theta$, c is the hypotenuse:
$\displaystyle \cos\theta=\frac{1}{c}\ \Rightarrow \ c=\frac{1}{\cos\theta}=\sec\theta$
