HelP!! Graphical Method of Solving Trig Eqns (1 Viewer)

[2opinion8d]

Is there any way u can solve this question without the graphical method

Find the points of intersection of the curves y = sin θ and y = cos θ
for 0 ≤ θ ≤ 2π and calculate the area between the two curves.
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I’m fine with calculating the area… but it is finding the points of intersection that really gets me frustrated. The first one’s obvious ( π / 4 ) as both eqns = 1/√2 at that point… but what about the second point… how accurate should i get it.
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Even with general questions involving the graphical method I’m always off the actual answer quite a bit.
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Can anyone help me out and offer and tips… thanX!

 

[roadrage75]

find points where sinθ = cosθ?

ie find where sinθ/cosθ = 1

ie fine where tanθ = 1 (cosθ doesn = 0)

there fore θ = π/4 and also, θ = 2π + π/4 --> here boh equations = -1/√2

(NOTE: we are looking for values where tanθ = 1, ie in 1st and 3rd quadrants.....)

 

[Forbidden.]

Graphical method of solving trigonometric equations ?

It's
Number of Intersections = Number of Solutions


It depends on your intervals you plotted on the x-axis of your graph

coz
π/2 = 1.6 (to 1 d.p) and π/4 = 0.8 (to 1 d.p)

OR

3π/8 = 1.2 (to 1 d.p) and π/4 = 0.8 (to 1 d.p)

I usually plot as accurate as 0.1~0.2 as my gap interval size.