Asked by Claire
Solve the following equation for 0<x<2Pi: (answer has to be in radians)
sec (x + [pi/10]) =-5
sec (x + [pi/10]) =-5
Answers
Answered by
Damon
Let y = x+pi/10
sec is 1/cos
1/cos(y) = -5
so cos y =-0.2
There are two quadrants where cos is negative, the second and the third.
Angle y will be pi -inverse cos of +0.2 and pi+inverse cos +.2
inverse cos .2 = 1.37 rad
so
y = pi +/- 1.37
y = 4.51 or 1.77
now get the two values of x from
x = y - 0.1 pi
sec is 1/cos
1/cos(y) = -5
so cos y =-0.2
There are two quadrants where cos is negative, the second and the third.
Angle y will be pi -inverse cos of +0.2 and pi+inverse cos +.2
inverse cos .2 = 1.37 rad
so
y = pi +/- 1.37
y = 4.51 or 1.77
now get the two values of x from
x = y - 0.1 pi
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