find all the solution to the equation: 12sin(2t)cos3(t)+20sin(2t)-3cos(3t)-5=0

how to find all the solution
in Trigonometry Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

The equation can be factorised:

4sin2t(3cos3t+5)-(3cos3t+5)=0=(4sin2t-1)(3cos3t+5)=0

Therefore 4sin2t=1 or 3cos3t=-5. cos cannot exceed 1 or be less than -1, so the second option is not a solution.

sin2t=0.25, so 2t=14.4775 degrees (approx) and t=7.24 degrees, also 187.24, 367.24, etc.

sin(180-2t)=0.25, so 180-2t=14.4775, 2t=180-14.4775=165.5225, t=82.76 degrees, also 262.76, 442.76, etc.

Adding or subtracting 180 degrees to these angles generates more solutions because of the periodic nature of sine.

 

 

by Top Rated User (1.2m points)

Related questions

1 answer
0=(t-6)*(-2t*-2t+3t-6)
asked Oct 25, 2019 in Algebra 1 Answers by Jordan Fourie | 637 views
1 answer
-6.2(2t+4)-2.4(3t-5) simplify the equation
asked Jan 28, 2013 in Statistics Answers by anonymous | 740 views
1 answer
solve the following equation (3t-5)/(t-1) = 2+(2t)/(1-t)
asked Aug 29, 2013 in Algebra 1 Answers by steve88 Level 1 User (180 points) | 1.1k views
1 answer
Combine like terms: 3t + 5 (3 + t) - 2t - 4
asked Dec 2, 2015 in Pre-Algebra Answers by anonymous | 1.0k views
1 answer
(t^2+3t/t-2)+(2t-14/t-2)
asked Jan 30, 2013 in Algebra 1 Answers by anonymous | 685 views
1 answer
-2t+(t-3)>3t+1
asked Jan 24, 2012 in Algebra 1 Answers by anonymous | 762 views
1 answer
Show that Y=ln|cos3/cosx|+5 is the solution to the initial value problem dy/dx=tanx, f(3)=5
asked Feb 25, 2019 in Calculus Answers by rubicube Level 1 User (160 points) | 1.3k views
1 answer
how do you solve 3t^4+2t^3-300t-50=0
asked Dec 30, 2011 in Algebra 2 Answers by anonymous | 732 views
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!

Most popular questions within the last 3000 days

  1. 50+50-25X0+2+2= (19)
  2. it takes 10 road workers 5 days to complete a road repair when working 2 hours a day.Working at the same pace,how many days will it take 2 people working 5 hours a day to finish it? (3)
  3. Solve 15 -1(12÷4+1)? (4)
  4. 8:4(5+2) (3)
  5. How can i represent 1/3; 3/3; 7/3; 10/3 and 15/3 on a number line? (1)

Most popular tags

87,516 questions
100,279 answers
2,420 comments
731,637 users