Question

which relationship in the triangle must be true?
a
c

b
c
b
a
sin(b) = sin(a)
sin(b) = cos(90 − b)
cos(b) = sin(180 − b)
cos(b) = cos(a)

Explanation:

Step1: Recall co-function identity

The co-function identity states $\sin(\theta) = \cos(90^\circ - \theta)$. For angle $B$, substitute $\theta = B$:
$\sin(B) = \cos(90^\circ - B)$

Step2: Verify other options

• $\sin(B)=\sin(A)$: Only true if $A=B$, not always true.
• $\cos(B)=\sin(180-B)$: $\sin(180-B)=\sin(B)$, so this would mean $\cos(B)=\sin(B)$, only true if $B=45^\circ$.
• $\cos(B)=\cos(A)$: Only true if $A=B$, not always true.

Answer:

$\boldsymbol{\sin(B) = \cos(90 - B)}$