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June 23rd, 2015, 08:43 AM  #1 
Newbie Joined: Jan 2014 Posts: 19 Thanks: 0  equal sign or approximation sign?
I want to solve the equation $\displaystyle 2\sin^2 \theta+2\sin\theta1=0$, $\displaystyle 0\leq\theta<2\pi$. Using the quadratic formula, I found one of the solutions to be $\displaystyle \theta=\sin^{1}( \frac{1+\sqrt{3}}{2})$. Which of the following ways of writing the numerical value of $\displaystyle \theta$ is correct? (i) or (ii)? (i) $\displaystyle \theta=0.3747$, (ii) $\displaystyle \theta\approx 0.3747$ Are both of them acceptable? I noticed that, in most trigonometric textbooks the numerical solution of a trigonometric equation is written using the equal sign (as in (ii)) even though the numerical answer has been rounded (questions didn't require us to round the answers). Why equal sign is used instead of approximation sign? In this case, does the equal sign mean "equal after rounded"? Last edited by skipjack; June 23rd, 2015 at 02:51 PM. 
June 23rd, 2015, 09:16 AM  #2 
Senior Member Joined: Jun 2015 From: England Posts: 915 Thanks: 271 
Hello, woo your equations don't come out. However the statement "correct to 3 dp (decimal places) or 3 sf (significant figures) or whatever should be used with the solution, not the approximation sign. This is because the sin(a) does equal some number correct to...... does this help? 
June 23rd, 2015, 09:22 AM  #3 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
I would write either $\theta=0.3747\ldots$ or $\theta\approx0.3747.$

June 23rd, 2015, 09:53 AM  #4 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,681 Thanks: 2659 Math Focus: Mainly analysis and algebra 
The distinction is only very slight. It's trivial enough to be called "picky" to my mind. But to be absolutely correct $\theta = 0.3747 \,\text{(to 4 d.p.)}$, $\theta = 0.3747 \,\text{(to 4 s.f.)}$ or either of CRGreathouse's formulations would be correct.

June 24th, 2015, 12:53 AM  #5 
Senior Member Joined: May 2015 From: Varanasi Posts: 110 Thanks: 5 Math Focus: Calculus 
You may write either but i think the solution is not right, it should be in radian or degree.And probably not less than 1.


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