if tanx = 1, then sinx = cosx ... the angle values of x where this is true is at x = pi/4 and 5pi/4, and those other angles coterminal with these two angles.
this is a fact that should be learned during a trig unit in precalculus.
I know from my text that tanx=1 when x=npi + pi/4 where n is and integer.
The text does not say how one should deduce that however (it's a caluclus text and perhaps this should be known from precalc?)
In any case, besides memorizing the values of x that make tanx=1, how would I got about finding these values algebraically? Or is it something that one really should memorize in the early stages?
thanks! my troubles in math (generally) stem from being a mature student (have not been in high school for over ten years) and having gone to a high school where the math teachers routinely failed to complete the syllabus each term from the equivalent of form 1 (roughly grade 7 in the North American system - i was 'educated' in a tiny island in the caribbean). So each year there would be concepts needed for the next year's course work that were never covered in class. This lead to an impression in my case that math was essentially magic.
Hence I have gaps in my knowledge that I need to fill, but because of the nature of these gaps I am not always aware of that which I am unaware...if that makes sense. In other words I don't know if there is a concept I should know that I do not know until I get to a question which assumes that previous knowledge.
Access to this forum and sites such as khan academy are the primary reasons i am capable of even passing first year calculus. I'm always amazed at how gracious people are when it comes to sharing math.
PS long live Herbert Gross, i love that guy
It should be routine to know the trig ratios of zero, 30, 45, 60 and 90 degrees, (and from which the ratios of 120, 135, 150 and so on are deduced).
For zero, 90, 180 and 270, picture a point moving around a unit circle. The cosine and sine of the associated angle are the x and y co-ordinates of the point respectively, the tangent is the ratio sine/cosine.
For 30 and 60 degrees, draw an equilateral triangle with side length 2. Draw a line from a vertex to the midpoint of the opposite side. Take one of the resulting triangles, it will have angles 30, 60, 90 degrees and with sides of lengths 2,1,sqrt(3) (making use of Pythagoras). Just read off whichever trig ratio you need, sine = opp/hyp etc.
For 45 degrees draw a 45,45,90 degree triangle with sides 1,1,sqrt(2) and again read off the ratios as required.