logo88
Answered

Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

solve 3-2cos²x-3sinx=0 for 0≤x≤360

Sagot :

olemakpadu
3-2(Cosx)^2 - 3Sinx = 0.

Recall (Sinx)^2 + (Cosx)^2  = 1.
Therefore  (Cosx)^2 =  1 - (Sinx)^2
Substitute this into the question above.

3-2(Cosx)^2 - 3Sinx = 0
3 - 2(1 - (Sinx)^2)  - 3Sinx = 0  Expand
3 - 2 + 2(Sinx)^2  -  3Sinx = 0
1 + 2(Sinx)^2  - 3Sinx  = 0  Rearrange
2(Sinx)^2 - 3Sinx + 1  = 0 
Let p = Sinx
2p^2  -  3p + 1  = 0    Factorise the quadratic expression
2p^2 - p - 2p +1 = 0
p(2p -1) - 1(2p -1) = 0
(2p-1)(p -1) = 0

Therefore  2p-1=0    or  (p-1) = 0
2p=0+1    or  (p-1) = 0
2p=1       or    p = 0 +1.
p=1/2       or  p = 1            Recall p = Sinx

Therefore Sinx = 1/2 or 1.
For  0<x<360

Sinx =1/2,  x = Sin inverse (1/2) , x = 30, 
                                   (180-30)- 2nd Quadrant = 150 deg
Sinx = 1,  x = Sin inverse (1) , x = 90

Therefore x = 30,90 & 150 degrees.

Cheers.
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.