SOLUTION: Evaluate the expression. {{{ cos(-x) }}}{{{ cot(x) }}}{{{ sin(-x) }}} A.) {{{ cos(x) }}} B.) {{{ -cos(x) }}} C.) {{{ cos^2(x) }}} D.) {{{ -cos^2(x) }}}

Algebra ->  Trigonometry-basics -> SOLUTION: Evaluate the expression. {{{ cos(-x) }}}{{{ cot(x) }}}{{{ sin(-x) }}} A.) {{{ cos(x) }}} B.) {{{ -cos(x) }}} C.) {{{ cos^2(x) }}} D.) {{{ -cos^2(x) }}}      Log On


   



Question 1058467: Evaluate the expression.
+cos%28-x%29++cot%28x%29++sin%28-x%29+
A.) +cos%28x%29+
B.) +-cos%28x%29+
C.) +cos%5E2%28x%29+
D.) +-cos%5E2%28x%29+

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

Memorize the 6 trig ratios for the negative angles:
(only the cosine and secant don't change the sign)

sin(-x) = -sin(x)
cos(-x) = cos(x)
tan(-x) = -tan(x)
sec(-x) = sec(x)
csc(-x) = -csc(x)
cot(-x) = -cot(x)

+cos%28-x%29cot%28x%29sin%28-x%29+%22%22=%22%22

+cos%28x%29cot%28x%29%28-sin%28x%29%5E%22%22%29+%22%22=%22%22

+-cos%28x%29cot%28x%29sin%28x%29+%22%22=%22%22

Use the identity cot%28theta%29=cos%28theta%29%2Fsin%28theta%29

+-cos%28x%29%2Aexpr%28cos%28x%29%2Fsin%28x%29%29sin%28x%29+%22%22=%22%22

+-cos%28x%29%2Aexpr%28cos%28x%29%2Fcross%28sin%28x%29%29%29cross%28sin%28x%29%29+%22%22=%22%22

+-cos%28x%29cos%28x%29+%22%22=%22%22

+-cos%5E2%28x%29+

Edwin