Question

for each of the trigonometric ratios in the table, determine an equivalent trigonometric ratio. select the boxes to identify the equivalent trigonometric ratios. select only one box per row. trigonometric ratio equivalent to sin(l) equivalent to cos(l) sin(q) cos(q) sin(r)

Explanation:

Step1: Recall co - function identities

In a right - triangle, if two angles $\alpha$ and $\beta$ are complementary ($\alpha+\beta = 90^{\circ}$), then $\sin(\alpha)=\cos(\beta)$ and $\cos(\alpha)=\sin(\beta)$.

Step2: Analyze the relationship between angles

In right - triangle $JKL$, $\angle K+\angle L = 90^{\circ}$, and in right - triangle $QRS$, $\angle R+\angle Q=90^{\circ}$.

Step3: Determine equivalent trigonometric ratios

1. For $\sin(Q)$:

• Since $\angle L$ and $\angle Q$ are complementary to angles in right - triangles such that if we assume the relevant angle relationships based on the general property of right - triangles and complementary angles, $\sin(Q)=\cos(L)$.

1. For $\cos(Q)$:

• $\cos(Q)=\sin(L)$.

1. For $\sin(R)$:

• Since $\angle R$ and $\angle L$ are in similar complementary - angle relationships in right - triangles, $\sin(R)=\sin(L)$.

Answer:

Trigonometric ratio	Equivalent to $\sin(L)$	Equivalent to $\cos(L)$
$\cos(Q)$	$\cos(Q)=\sin(L)$
$\sin(R)$	$\sin(R)=\sin(L)$