posted by .

find all solutions in interval [0,2pi]

tan²x = -3/2 secx

This question may look tricky, but its actually quite simple.

First: rearrange the pythagorean identity tan²x+1=sin²x so that it reads tan²x=sin²x-1

Then replace the tan²x in the original problem with the sin²x-1 that you got from rearranging the pythagorean identity

Now the equation should read:

Next bring the (-3/2)secx to the other side of the equation to make it read:

sin²x+ (3/2)secx -1

Look familiar?

Yes! It is a quadratic. So you should set it equal to zero and factor.

I used the quadratic formula to get the two answers: -2 and .5

Then look on the unit circle and ask yourself: Where is the sec -2? Where is the sec .5?

Answer your questions by finding the points on the unit circle. Use the radians as your answers and don't forget to add 2(pi)n or (pi)n respectively

Let me know if you need more exact instructions


Im still stuck on the following steps i have no idea what im doing here..........sorry this is the section that ive had sooo much trouble in.

I would do it this way:

tan²x = -3/2 secx

sin²x/cos²x = -3/2cosx

multiply both sides by cosx

sin²x/cosx = -3/2 cross-multiply
2sin²x = -3cosx then by the Pythagorean identity
2(1-cos²x) + 3cosx = 0
2cos²x - 3cosx - 2 = 0
(2cosx+1)(cosx-2) = 0
so cosx = -1/2 or cosx = 2, the last is not possible because cosine is between -1 and 1

then cosx=-1/2 means the angle is in the second or third quadrants.
x = 120º or x = 300º


Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. trig

    Verify the trigonometric identity: [(1–sin²x)/sin²x]–[(csc²x–1)/cos²x]= -tan²x I can't figure this out.
  2. trig

    Verify the trigonometric identity: [(1–sin²x)/sin²x]–[(csc²x–1)/cos²x]= -tan²x I still can't figure this out.
  3. pre-calc

    tanx= -12/5 x in Q 2. find sin2x= cos2x= tan2x=
  4. pre-calculus

    tanx= -12/5 x in quadrant 2 find; sin2x= cos2x= tan2x=
  5. Math please help quick

    Which of the following are identities? Check all that apply. (Points : 2) sin2x = 1 - cos2x sin2x - cos2x = 1 tan2x = 1 + sec2x cot2x = csc2x - 1 Question 4. 4. Which of the following equations are identities?
  6. Trig help

    Can someone help me find ALL solutions in the interval [0,2π) for the given equations. Please show work. 1) sin2x = sin2x 2) tan2x +tanx = 0
  7. Math

    Solve the equation on the interval [0, 2π). tan2x sin x = tan2x would it be 0, pi/2 ?
  8. maths

    solve: tanx+tan2x+√3tanx tan2x=√3 (0<=x<=360)
  9. math

    sin2x − cos2x − tan2x = 2sin2x − 2sin4x − 1/ 1 − sin2x for x = 45
  10. trig

    secx = 4 in Q2 find sin2x,cos2x,tan2x

More Similar Questions