Final Answer:
If sin(t)=-(3)/(7), then:
sin(-t) = -sin(t)= 3\7
csc(-t) = 1/sin(-t) = -1/(3/7) = -7/3
Step-by-step explanation:
To find sin(-t) and csc(-t), we use the following properties of trigonometric functions:
1. If t is an angle, then -t is also an angle. The sign of the angle determines whether it is measured in a counterclockwise or clockwise direction. Since we are given sin(t) = -(3)/(7), we know that this angle is measured in a counterclockwise direction. Therefore, to find sin(-t), we simply replace t with -t:
sin(-t) = sin(measured in the opposite direction) = -sin(t)
2. To find csc(-t), we use the fact that csc(x) = 1/sin(x). However, since we are finding csc(-t), we need to be careful about the sign of sin(-t):
csc(-t) = 1/sin(-t) = -1/(3/7) = -7/3