Solving for 't': Tips and Tricks for Navigating Tricky Equations

  • Thread starter Thread starter mesa
  • Start date Start date
AI Thread Summary
The discussion focuses on solving the equation 1/2 + pi/4 = (9.8/4)cos(2t) + sin(2t) for 't'. Participants express frustration with their attempts, noting that trigonometric equations often require iterative methods for solutions. A suggested approach involves rewriting the right-hand side in the form A*cos(2t + ω), utilizing trigonometric addition formulas to derive numerical values for amplitude (A) and phase (ω). This method aims to simplify the equation for easier resolution. Overall, the conversation highlights common challenges and strategies in tackling complex trigonometric equations.
mesa
Gold Member
Messages
694
Reaction score
36

Homework Statement



Solve for 't'
1/2+pi/4 = (9.8/4)cos2t + sin(2t)

The Attempt at a Solution



I don't know what's wrong with my brain today but every attempt came up empty :P
 
Physics news on Phys.org
Absent some Jedi mind tricks, most trig equations require an iterative method of solution.
 
SteamKing said:
Absent some Jedi mind tricks, most trig equations require an iterative method of solution.

Nice to know the brain is still functioning properly, it's been a long day :P
 
mesa said:

Homework Statement



Solve for 't'
1/2+pi/4 = (9.8/4)cos2t + sin(2t)

The Attempt at a Solution



I don't know what's wrong with my brain today but every attempt came up empty :P

Re-write the right-hand-side in the form A*cos(2t + ω), where A is the amplitude and ω is the 'phase'. Use the trigonometric addition formulas to (eventually) get numerical values for A and ω.
 

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
View full post »

Thread 'Making the denominator of a certain fraction real'

Essentially I just have this problem that I'm stuck on, on a sheet about complex numbers: Show that, for ##|r|<1,## $$1+r\cos(x)+r^2\cos(2x)+r^3\cos(3x)...=\frac{1-r\cos(x)}{1-2r\cos(x)+r^2}$$ My first thought was to express it as a geometric series, where the real part of the sum of the series would be the series you see above: $$1+re^{ix}+r^2e^{2ix}+r^3e^{3ix}...$$ The sum of this series is just: $$\frac{(re^{ix})^n-1}{re^{ix} - 1}$$ I'm having some trouble trying to figure out what to...
View full post »

Similar threads

Prove the trigonometry identity and hence solve given problem
Replies
5
Views
2K
How Do You Solve for t When Point E Lies on Line CD?
Replies
10
Views
2K
Math Derivation: Solve for t - Calc 1 Help
Replies
1
Views
2K
Solution to a sixth grade (degree 6) equation
Replies
7
Views
3K
Solving equations of the form ##a\sin\theta+b\cos\theta = c##
Replies
2
Views
2K
Linear Trig Equations: Solving sin(x + pi/4) = √2 cos x
Replies
6
Views
2K
How to solve this math problem: Two simultaneous trig equations
Replies
8
Views
2K
Solving: 3cos(t)-sin(t)cos(t)=0
Replies
3
Views
2K
How Can You Solve This Modulus Equation with Square Roots and Absolute Values?
Replies
1
Views
2K
Half Angle Formula for Tangent
Replies
15
Views
3K

Hot Threads

Recent Insights

Back
Top