Which of the following statements accurately describes a difference between the graphs of \( f(x)=\sin (x) \) and \( g(x)=\sin (-x) \) ? Statement \#1: If \( (x, y) \) is a point in \( f(x) \), then \( (x,-y) \) is a point in \( g(x) \). Statement \#2: The function \( g(x) \) is the same as \( f(x) \). Statement \#3: If \( (x, y) \) is a point in \( f(x) \), then \( (-x,-y) \) is a point in \( g(x) \). (1 point) Statement \# \( \square \) is correct.

b) \( \csc \theta=\frac{\cos ^{2} \theta+\sin ^{2} \theta}{\sin \theta} \)

c) \( \frac{\sin ^{2} \theta-3 \sin \theta+2}{\sin ^{2} \theta-1}=\frac{\sin \theta-2}{\sin \theta+1} \)

1. Los ángulos de elevación de un globo desde dos puntos \( A \) y \( B \) al nivel del suelo son \( 24^{\circ} \) y \( 48^{\circ} \), respectivamente. Los puntos \( A \) y están a 4 kilometros entre si, y el globo está entre los puntos, en el mismo plano vertical.

11. Prove the following identities. a) \( \sin \theta \cos \theta \cot \theta=1-\sin ^{2} \theta \)

9. If \( \cos \theta=-\frac{1}{\sqrt{2}} \) and \( 0^{\circ}<\theta<360^{\circ} \) determine the possible values of \( \theta \). Include a diagram. \( \checkmark \)