Draw a right triangle situated as if it's in the third quadrant of a plane with its vertex at the origin. The horizontal part is x, or -4. The vertical part is -7.
Using the Pythagorean theorem, we find that the hypotenuse is √65, which cannot be simplified because it's the product of two primes, 5 and 13.
Using SOHCAHTOA, we find the cos of this angle is -4/√65. Since sec is the reciprocal of cos, the secant is -(√65)/4.
I hope this helps! Let me know if you have another question about this, and have fun mathing!
LizZ.
