Can You Solve 0.221=sinθcosθ for θ Without a Calculator?

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AI Thread Summary
To solve the equation 0.221 = sinθcosθ, one can utilize the identity sin(2θ) = 2sin(θ)cos(θ), which simplifies the problem. By rewriting the equation as 0.1105 = sin(2θ), it becomes easier to solve for θ. The next step involves finding the inverse sine of 0.1105, which can be done using a calculator or trigonometric tables. If a calculator is not available, one can estimate the angle using known values of sine. This approach provides a clear path to determine the value of θ without relying solely on computational tools.
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Homework Statement



i have the equation 0.221=sinθcosθ. I want to find the vaue of θ. Is there anyway i can solve this with or without a calculator? (solver function on both my calculator and wolfram alpha do not work)

thanks
 
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hahaha158 said:

Homework Statement



i have the equation 0.221=sinθcosθ. I want to find the vaue of θ. Is there anyway i can solve this with or without a calculator? (solver function on both my calculator and wolfram alpha do not work)

thanks

sin(2θ)=2*sin(θ)*cos(θ). Try using that.
 

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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