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How do you find the area between the two consecutive points of intersection of y=sinx and y=cosx?

Answer 1

Luke Alvarez

#2sqrt2# areal units

#sinx = cos x at x = pi/4, 5pi/4, ...#

The area in between, within two consecutive points of intersection #x = pi/4 and x= 5pi/4#

#=int (sin x - cos x) d x#, between the limits

#=[-cosx-sinx]#, between the limits

#=[(-sin(5pi/4)-cos(5pi/4)+(sin(pi/4+cos(pi/4)]#

#=[-(-1/sqrt2-1/sqrt2)+(1/sqrt2+1/sqrt2)]#

#=4/sqrt2=2sqrt2#, areal units.-

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Answer 2

Evelyn Agard

To find the area between the two consecutive points of intersection of (y = \sin(x)) and (y = \cos(x)), follow these steps:

Determine the points of intersection by setting the two equations equal to each other and solving for (x).
Calculate the difference between the x-coordinates of the two consecutive points of intersection. This represents the width of the region.
Integrate the absolute difference between (\sin(x)) and (\cos(x)) with respect to (x) over the interval of the width determined in step 2.
The result of the integration will give you the area between the curves over the specified interval.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.