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