SOLUTION: Which answer is equal to this expression? {{{ sin(-x)/cos(-x) }}} A.) {{{ tan(x) }}} B.) {{{ tan(-x) }}} C.) {{{ -tan(x) }}} D.) B and {{{ C }}}

Algebra ->  Test -> SOLUTION: Which answer is equal to this expression? {{{ sin(-x)/cos(-x) }}} A.) {{{ tan(x) }}} B.) {{{ tan(-x) }}} C.) {{{ -tan(x) }}} D.) B and {{{ C }}}      Log On


   

Question 1058392: Which answer is equal to this expression?
+sin%28-x%29%2Fcos%28-x%29+
A.) +tan%28x%29+
B.) +tan%28-x%29+
C.) +-tan%28x%29+
D.) B and +C+
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
You need to know and recognize the definition for .... for tangent function.

The choices presented are an attempt to trick you regarding the evenness of any trigonometric functions. Make reference to the unit circle to help think through this clearly. Is the answer, just B? Or is it B and C ?

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Create a general example for yourself and refer to the point on the Unit Circle. Sketch a point in, for example quadrant number 3. If x is positive, then -x is negative, so rotation would go clockwise to reach into quadrant 3.
Sine of -x is same as -sine of x. So you have sin%28-x%29=-sin%28x%29.
cos%28-x%29=cos%28x%29.
Again, you look at your -x as the point ON the Unit Circle.

Look at given expression now.
sin%28-x%29%2Fcos%28-x%29; you know that this will be tan%28-x%29. What else might it be, according to the facts discussed above?