SOLUTION: I have absolutely no idea how to do this. Thank you in advance! Find the exact value of {{{ tan(cos^-1(-3/5)) }}}

Algebra ->  Trigonometry-basics -> SOLUTION: I have absolutely no idea how to do this. Thank you in advance! Find the exact value of {{{ tan(cos^-1(-3/5)) }}}      Log On


   

Question 985833: I have absolutely no idea how to do this.
Thank you in advance!
Find the exact value of +tan%28cos%5E-1%28-3%2F5%29%29+
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
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Find the exact value of tan%28arccos%28-3%2F5%29%29.
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Let  alpha = arccos%28-3%2F5%29.     (Notice that  alpha  lies in the segment  [0, pi]).   We need to find  tan%28alpha%29.

Then  cos%28alpha%29 = -3%2F5,

sin%28alpha%29 = sqrt%281+-+cos%5E2%28alpha%29%29 = sqrt%281+-+%28-3%2F5%29%5E2%29 = sqrt%281+-+%289%2F25%29%29 = sqrt%28%2825-9%29%2F25%29 = sqrt%2816%2F25%29 = 4%2F5.

Now   tan%28alpha%29 = sin%28alpha%29%2Fcos%28alpha%29 = 4%2F5:%28-3%2F5%29 = -4%2F3.