SOLUTION: Given that sin&#952; is equal negative 3 over 4 and cos&#952; < 0, find the exact value of tan&#952;.

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Question 1085573: Given that sinθ is equal negative 3 over 4 and cosθ < 0, find the exact value of tanθ.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
You know that,
sin%5E2%28theta%29%2Bcos%5E2%28theta%29=1
%28-3%2F4%29%5E2%2Bcos%5E2%28theta%29=1
9%2F16%2Bcos%5E2%28theta%29=1
cos%5E2%28theta%29=16%2F16-9%2F16
cos%5E2%28theta%29=7%2F16
cos%28theta%29=0+%2B-+sqrt%287%29%2F4
Since you know cos%28theta%29%3C0,
cos%28theta%29=-sqrt%287%29%2F4
So,
tan%28theta%29=sin%28theta%29%2Fcos%28theta%29
tan%28theta%29=%28-3%2F4%29%2F%28-sqrt%287%29%2F4%29
tan%28theta%29=3%2Fsqrt%287%29
tan%28theta%29=%283%2F7%29sqrt%287%29