PreCalculus
posted by Sharon .
Find the solutions for sec^2x+secx=2 that fit into the interval [0, 2pi]
I figured out that pi/3 (after factoring and switching things around) was a solution, but then I got stuck on cos x = 1/3.

no!
why don't you factor it with the secant as is
sec^2 x + secx  2 = 0
(secx + 2)(secx1) = 0
secx = 2 or secx = 1
cosx = 1/2 or cosx = 1
from cosx = 1/2, x = 120º (2pi/3) or 240º (4pi/3)
or
from cosx = 1, x = 0 or 360º (0 or 2pi) 
The answers in the back of my book are pi/3,pi, and 5pi/3
Respond to this Question
Similar Questions

solving trig. equations
tan(3x) + 1 = sec(3x) Thanks, pretend 3x equals x so tanx + 1 = secx we know the law that 1 + tanx = secx so tanx + 1 becomes secx and... secx = secx sec(3x) = sec(3x) [just put 3x back in for x you don't really have to change 3x … 
PreCalculus
cos^2(x) + sin(x) = 1  Find all solutions in the interval [0, 2pi) I got pi/2 but the answer says {0, pi/2, pi} Where does 0 and pi come from for solutions? 
pre cal
Find all solutions in the interval[0,2pi),cos x/2sinx=0 
precalculus
solve cos 2x=secx for 0(<=)x<2pi using trigonometric identities. 
PreCalc/Math
Use factoring, the quadratic formula, or identities to solve cos(x)+1=sin^(2)x. Find all solutions on the interval [0, 2pi) 
Math
Can I please get some help on these questions: 1. How many solutions does the equation,2sin^2 2 θ = sin2θ have on the interval [0, 2pi]? 
Trig verifying identities
I am having trouble with this problem. sec^2(pi/2x)1= cot ^2x I got : By cofunction identity sec(90 degrees  x) = csc x secx csc1 = cot^2x Then split sec x and csc1 into two fractions and multiplied both numerator and denominators … 
PreCalculus
Can someone please explain on how to solve this equation so I can do the others that are similar to this one? 
math
find all solution to the equation 3 cos(x+4)=1. in the interval of 0<x<2pi This is what I got: arccos (1/3)+4 but I cant figure the rest out Solve the following equation in the interval [0, 2pi]. (sin(t))^2=1/2. Give the answer … 
Precalculus
Prove the following identities. 1. 1+cosx/1cosx = secx + 1/secx 1 2. (tanx + cotx)^2=sec^2x csc^2x 3. cos(x+y) cos(xy)= cos^2x  sin^2y