Question

What is the y-value of sin(x) when x= -360°?

Answer 1

For what x-value(s) does cos(x) = 0?

Answer 2

@JFraser

Answer 3

@johnweldon1993

Answer 4

so for very first question you are dealing with a function \(\large\color{black}{{\rm y}=\sin(x)}\)

when \(x=360\) what do you get for \( \rm y\) ? Plug in 360 instead of \(x\) into the function.

Answer 5

do you know what \(\sin(360)\) is equivalent to?

Answer 6

0 @SolomonZelman

Answer 7

wait 360 is negative.. @SolomonZelman

Answer 8

sin(360)=0

you were correct

Answer 9

now, for the second question you need to find all solutions cos(x)=0

there is an infinity of these solutions, but they all follow certain pattern.

Answer 10

@Butterfield1215

Answer 11

I will give an example of how to generate this pattern.
---------------------------------------------
((here goes the question))
`What values of x are solutions sin(x)=0 ?`

((here is the solutions))
At first, we know that \(\sin(0)=0\), and therefore \(x=0\) is one possible solution.

then there are all co-terminal angles (each \(360^\circ\) you will come to the same value, because the circle/cycle restarts).



so, every +360 degrees (anticlockwise) or every -360 (going clockwise) you meet a condition of sin(x)=0.

So, your pattern is

\(\large\color{black}{ \displaystyle x= k\times 360;~~~k\in{\bf Z} }\)