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If theta is an angle in quadrant IV such that sine(theta)=-5/6, find secant and tangent of theta

Guest Jun 13, 2017
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We can use the Pythagorean identity to find   cos θ   .

 

 sin2 θ + cos2 θ  =  1         Replace   sin θ   with   -5/6

(-5/6)2  + cos2 θ  =  1

 25/36  + cos2 θ  =  1        Subtract   25/36   from both sides of the equation.

cos2 θ  =  11/36                Cos is positive in Quad. IV , so take the positive square root of both sides.

cos θ    =  √11 / 6

 

sec θ  =  1 / cos θ                   Secant is the reciprocal of cosine.

sec θ  =  1 / ( √11 / 6 )

sec θ  =  6 / √11

 

tan θ  =  sin θ / cos θ               Plug in the values we've found for   sin θ   and   cos θ  .

tan θ  =  ( -5/6 ) / ( √11 / 6 )

tan θ  =  ( -5/6 ) * ( 6 / √11 )

tan θ  =   - 5 / √11

hectictar  Jun 13, 2017
edited by hectictar  Jun 13, 2017

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