Solving Complex Homework Equations

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The discussion revolves around solving the equation 1 = 121 sinθ * cosθ + 592.9 (cos²θ). The user attempts to simplify the equation using the identity for sin(2θ) and expresses it as 1 = 60.5 sin 2θ + 592.9 (cos²θ). There is uncertainty about the next steps, particularly in eliminating sinθ * cosθ. A suggestion is made to rewrite cos²θ in terms of cos(2θ) to facilitate the solution. The conversation highlights the importance of using trigonometric identities to simplify complex equations effectively.
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Homework Statement


1 = 121 sinθ *cosθ + 592.9 (cos²θ)


Homework Equations





The Attempt at a Solution



1= 60.5 * 2 *sin θ *cosθ + 592.9 (cos²θ)
1= 60.5 sin 2θ + 592.9 (cos²θ)
1-60.5 sin 2θ / cos θ cos θ= 592.9

am i doing it rite? i don't know what to do
 
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Use sin^2 + cos^2 =1
 
but i don't know how to get rid of sin θ *cosθ
 
You wrote sin(theta)*cos(theta) in terms of sin(2*theta). Write cos(theta)^2 in terms of cos(2*theta).
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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