For 10 points, name this trig function that equals the length of the adjacent side over the hypotenuse for an acute angle in a right triangle.
In the exciting world of differential equations, the Laplace transform of this function equals s over the quantity s-squared plus a-squared. The hyperbolic form of this function is found in the equation of a catenary and equals e to the x plus e to the negative x all over two. In calculus, the Maclaurin series for it begins one minus quantity x-squared over two factorial. Its namesake law and the Pythagorean theorem are equivalent when this function is zero. The derivative of this function is negative sine, and its reciprocal is secant. For 10 points, name this trig function that equals the length of the adjacent side over the hypotenuse for an acute angle in a right triangle.
In the exciting world of differential equations, the Laplace transform of this function equals s over the quantity s-squared plus a-squared.
cosine [or cos] 