Solving a Trigonometric Equation to Hit a Moving Target

AI Thread Summary
To solve the trigonometric equation 40sinθcosθ - 10sinθ - 1 = 0 without a calculator, one approach is to substitute cosθ with √(1 - sin²θ). Alternatively, transforming the equation using tan(θ/2) can simplify the process. Both methods allow for a manual solution to find the angle needed to hit a moving target. Engaging with these techniques can lead to a clearer understanding of the problem. Exploring these substitutions is essential for solving the equation effectively.
peanut648
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So the orginial question asked what angle to fire a gun to hit a moving target, and i got all the way to 40sinθcosθ-10sinθ-1 = 0, but we aren't supposed to use calculators so how would you solve this by hand. Thanks!
 
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Hi peanut648! Welcome to PF! :smile:

Either use cosθ = √(1 - sin2θ), or write everything in terms of tan(θ/2). :wink:
 

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