MAT 112 Quiz #5
Name:________________________Section 6.3 25-36
(4pts)
Find all solutions of the equation in the interval [0, 2p ) using analytic techniques (show your work for credit)
tan2 x - 1 = 0.
tan2 x = 1
tan x = + 1, the angle associated with a tangent value of 1 is p /4, the period of the tangent function is p , and we have solutions in all four quadrants so
x = p/4, 3p/4, 5p/4, 7p/4 are our solutions on the interval [0, 2p ).
Section 6.3 25-36
Find all solutions of the equation in the interval [0, 2p ) using your calculator
sec x csc x = 2 csc x.
Method 1: Graph sec x csc x - 2 csc x = 0 in the window
(3pts) xmin = 0, xmax = 2p , ymin = -10, ymax = 10
Circle your solutions
and give your solutions
accurate to 3 decimals
The solutions are the zeros of the function, occurring at x = 1.047 and x = 5.236.
Method 2: Graph y1 = sec x csc x, y2 = 2 csc x in the same window
(3pts) xmin = 0, xmax = 2p , ymin = -10, ymax = 10
Circle your solutions
and give your solutions
accurate to 3 decimals
The solutions are the intersections of the functions, occurring at x = 1.047 and x = 5.236.
Essential Trogonometry, Math Links
by Jack Tompkins