SOLUTION: If the sine of an angle is negative, which other trigonometric functions will definitely have negative values?

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Question 296672: If the sine of an angle is negative, which other trigonometric functions will definitely have negative values?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If the sine of an angle is negative, then the cosine of that same angle may be negative, but it could also be positive. So let's move on.


If the sine of an angle is negative, then the tangent of that angle will be negative only if the cosine of that angle is positive. So again we don't have a guarantee.


If the sine of an angle is negative, then the cosecant (defined by csc%28x%29=1%2Fsin%28x%29 ) will definitely be negative since '1' is positive and dividing a positive by a negative will be negative.


If the sine of an angle is negative, then the secant (defined by sec%28x%29=1%2Fcos%28x%29 ) will only be negative if the cosine of that angle is negative. So no guarantees here.


Finally, if the sine of an angle is negative, then the cotangent (defined by cot%28x%29=1%2Ftan%28x%29=cos%28x%29%2Fsin%28x%29 ) will only be negative if the cosine of that angle is positive. So no guarantees here.


So if sine of an angle is negative, then the only function that will definitely be negative as well is the cosecant function.