SOLUTION: If cosθ = 1/5 and θ is in Quadrant IV, find tanθsecθ + cscθ

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Question 847640: If cosθ = 1/5 and θ is in Quadrant IV, find tanθsecθ + cscθ
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
cos%28theta%29+=+1%2F5
theta+=+cos%5E-1%281%2F5%29
theta+=+78.463 degrees.
Notice that 78.463 is in our first quadrant, so we need to make an angle of 78.463 that resides in the 4th quadrant. Here's the important step. MAKE SURE that you make the angle with respect to the x-axis. So, we are looking for the angle 360. Note that if we subtract 78.463 from 360, we will be in the 4th quadrant. We would not add as that would put us in Q1. Following this
theta+=+360+-+78.463+=+281.537 degrees.
tan(281.537 degrees)*sec(281.537 degrees) + csc(281.537 degrees) = -25.52