Loganap17idn
Answered

Join the IDNLearn.com community and start getting the answers you need today. Join our knowledgeable community to find the answers you need for any topic or issue.

Solve the equation 3 tan^2

x − 5 tan x − 2 = 0 for 0° ≤ x ≤ 180°

please explain​

Solve The Equation 3 Tan2x 5 Tan X 2 0 For 0 X 180please Explain class=

Sagot :

Isabellakosteridn
we can replace tanx with y this making the equation
3y^2 - 5y - 2 = 0 so we solve for y
Δ = b^2 - 4ac (a=3 b=-5 c=-2)
Δ = 25 + 24 = 49
y1 = (5 + 7) / 6 = 12/6 = 2
y2 = (5 - 7) / 6 = -2/6 = -1/3
since tan is positive in the first and third quadrant and according to the question x belongs somewhere in the first two quadrants the following is true
for y1 = tanx = 2 only applies for the first quadrant ( from 0° to 90°) while for y2 = tanx = -1/3 it can only apply for the second quadrant (from 90° to 180°). i hope this made sense because english is not my first language.
Your presence in our community is highly appreciated. Keep sharing your insights and solutions. Together, we can build a rich and valuable knowledge resource for everyone. Thank you for visiting IDNLearn.com. We’re here to provide clear and concise answers, so visit us again soon.