Inverse Trig (1 Viewer)
- Thread starter Petyo
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Of course. How silly of me. Values of cos can only vary from -1 to 1.
bored of sc
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The domain of inverse cosine is -1 < x < 1.
When you sub in x = -1, y = -pi
When you sub in x = 0 or 1, y = 0
But when you sub in say x = 1/2, y = pi/6
So it's confusing.
Ostentatious
jfK1c45g2f4Of56Eyd4f57cxZ
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Try using Graphmatica to graph it. It's totally trippy.
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Since the domain is -1 ≤ x ≤ 1, what you would typically do is substitute the end points of the domain to find the range. However, this assumes that the function you're dealing with is monotonic increasing or decreasing (i.e. has no turning points).
In this particular question, there happens to be a maximum turning point. The problem is that you can't really find the roots of this equation:
}{dx}=\cos^{-1}x-\dfrac{x}{\sqrt{1-x^2}}=0)
to determine the maximum turning point. So the exact upper limit is hard to find.
In this particular question, there happens to be a maximum turning point. The problem is that you can't really find the roots of this equation:
to determine the maximum turning point. So the exact upper limit is hard to find.
gurmies
Drover
What would happen if you were to approximate the root of that equation and keep approximating and subbing in, and observe what it approaches? Should in theory approach pi/2?Since the domain is -1 ≤ x ≤ 1, what you would typically do is substitute the end points of the domain to find the range. However, this assumes that the function you're dealing with is monotonic increasing or decreasing (i.e. has no turning points).
In this particular question, there happens to be a maximum turning point. The problem is that you can't really find the roots of this equation:
to determine the maximum turning point. So the exact upper limit is hard to find.
Petyo
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Where did you get these figures from?
Btw In class my teacher 'solved' this question by making a table of values. She has always been so unreliable...
graphmatica
the range would be the inverse of cosx
cosx:
domain: 0≤ x≤ pi
range: -1≤y≤1
therefore the inverse is:
xcos^-1 is
domain:-1≤x≤1
range:0≤y≤pi
gurmies
Drover
gurmies
Drover
what's hard 2 understand lol
u just swap the range and domain around when it comes 2 inverse =p
gurmies
Drover
Look at the graph above, the x dilates it.
gurmies
Drover
=)^ooooooooooooo i see