Question 851835: Find sin theta if sec theta =-8/5 and tan theta <0
Answer by Seutip(231)   (Show Source):
You can put this solution on YOUR website! Since tan and sec is negative therefore it is in quadrant 2, wherein only sin and csc are positive. :)
sec = -8/5 therefore,
cos = -5/8 because cos is the reciprocal of sec,
It is stated in the Pythagorean identities that,
cos^2+sin^2 =1
Therefore,
sin^2 =1-cos^2
Substitute,
sin^2 =1-(-5/8)^2
sin^2 =1-(25/64)
sin^2 =(64/64)-(25/64)
sqrt(sin^2) = sqrt(39/64)
sin = sqrt39/8
That is the value of sin squareroot of 39 over 8, hope that helps! :)
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