Question

Help

Answer 1

for part I: the zero product property tells us that if A*B = 0 then A = 0 and B = 0, use this logic to set up your two equations

Answer 2

(sec x-1)(cosx-sqrt2/2)=0

Answer 3

notice how we took the equation A*B = 0 and split it into two equations, A = 0 and B = 0

see if you can split your equation into two equations

Answer 4

(sec x-1)=0
(cosx-sqrt2/2)=0

Answer 5

like that

Answer 6

yes, that's it for part I

for part II: we have sec(x) - 1 = 0

and solving for sec(x) we get sec(x) = 1

how would we re-write sec(x) in terms of a sin, cos, or tan function?

Answer 7

it would be the inverse again right

Answer 8

be careful, it's not asking you to solve for x, just re-write sec(x) in terms of sin, cos, or tan

Answer 9

sec(x) = 1/cos(x) ---> this is very important to know

so 1/cos(x) = 1 is your sol'n for part II

Answer 10

anyway for part III you just need to solve

1/cos(x) = 1 and (cos(x)-sqrt2/2)=0

for x

Answer 11

using the unit circle

Answer 12

x=+2pi

x=pi/4 and 7pi/4

Answer 13

very close but 7pi/4 is not a sol'n since that's -sqrt(2)/2

Answer 14

-7pi/4?

Answer 15

oh wow i'm silly yeah it is 7pi/4, I was looking at 5pi/4 for some reason ;-:

Answer 16

anyway, we just need to add in our 2pi*n condition to gives us

2pi*n, 7pi/4 +/- 2pi*n, pi/4 +/- 2pi*n

Answer 17

anyway that's it