Question

Question Part
Points
Submissions Used
Solve the following equation, giving the exact solutions which lie in [0, 2π). (Enter your answers as a comma-separated list.)

tan2(x) =
3
2
sec(x)

Answer 1

\[\tan^2(x)= (3/2)\sec(x)\] here is the equation better

Answer 2

\[\large \tan^2(x)= \frac{3}{2}\sec(x)\]


\[\large \sec^2(x)-1= \frac{3}{2}\sec(x)\]


\[\large z^2-1= \frac{3}{2}z\]


\[\large 2(z^2-1)= 3z\]


\[\large 2z^2-2= 3z\]


\[\large 2z^2-2-3z = 0\]


\[\large 2z^2-3z-2 = 0\]


Now use the quadratic formula to solve for z. Tell me what you get.

Answer 3

ok sec

Answer 4

I get z = -(1/2), 2

Answer 5

so this means that

sec(x) = -1/2 or sec(x) = 2

because z = sec(x)

Answer 6

solve each equation for x

Answer 7

one of those equations has no solutions at all

Answer 8

I'm confused on the next step

Answer 9

sec(x) = -1/2

1/cos(x) = -1/2

cos(x) = -2

what's next?

Answer 10

1/cos(2)

Answer 11

im guessing im wrong

Answer 12

use the unit circle and tell me when cos(x) = -2 is true

Answer 13

it doesn't exist right?

Answer 14

good, there are no solutions

Answer 15

sec(x) = 2

1/cos(x) = 2

cos(x) = 1/2

what are the solutions here?

Answer 16

pi/3 , 5pi/3 ?

Answer 17

good, those are your two solutions

Answer 18

yay... thank you soo much!

Answer 19

you're welcome