basic question on working out solutions of cosine angle

[Sonal7]

Its working out the solutions of a cosine angle. Here is the answer. The question asks you to find the solutions to sin2x-tanx =0.
I understand the working but I can figure out how they worked out the solutions to cos 1/sqrt2. I know that one solution is 45 degrees, then they have added 180 to
get the next one 225. But graphically I cant see. Sorry if this is GCSE level stuff. According to the graph the next solution is 270+45 so 315. I think its a mistake?



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[Deleted member 4993]

Its working out the solutions of a cosine angle. Here is the answer. The question asks you to find the solutions to sin2x-tanx =0.
I understand the working but I can figure out how they worked out the solutions to cos 1/sqrt2. I know that one solution is 45 degrees, then they have added 180 to
get the next one 225. But graphically I cant see. Sorry if this is GCSE level stuff. According to the graph the next solution is 270+45 so 315. I think its a mistake?



:View attachment 17852View attachment 17853

You are correct.
cos(A) = cos(360 - A)

 

[Sonal7]

Sorry to ask such a dumb question, but if you dont get the basics right then there is no hope of learning harder stuff.

 

[lev888]

Sorry to ask such a dumb question, but if you dont get the basics right then there is no hope of learning harder stuff.

You can also use Wolfram Alpha to verify answers:

sin2x-tanx =0 - Wolfram|Alpha

Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels.

www.wolframalpha.com

 

[topsquark]

@Sonal7: Two things.
1) Perhaps this will help a bit. Your second factor is [math]cos(2x) = 2 ~ cos^2(x) - 1[/math] so what you want to solve is [math]cos(2x) = 0[/math]. Hopefully you'll be able to see the solutions to this one better.

2) Just an FYI. In step three you multiplied both sides of the equation by [math]cos^2(x)[/math]. That means we need to eliminate any value of x that makes cos(x) = 0. As it happens none of your solutions do that but that one slips by many people. It's a good thing to check.

-Dan