Question

How do you find the exact trig value for this and how do you know whether its negative or positive given -1290 degrees?

Answer 1

`sin(-1290^o)=1/2` `color(white)("XXXX")` `cos(-1290^o)= -sqrt(3)/2` `color(white)("XXXX")` `tan(-1290^o)= -1/sqrt(3)`

Explanation:

`-1290^o` represents `3` complete cycles
`color(white)("XXXX")`plus half a cycle
`color(white)("XXXX")`plus `30^o`
`color(white)("XXXXXXXX")`(all in clockwise direction)

So`-1290^o`
`color(white)("XXXX")`has a reference angle of `30^o`
`color(white)("XXXX")`and is in Quadrant II (`rArr` only `sin` is positive based on CAST system)

`30^o` is one of the standard angles but see image (below) for clarification if necessary.