The curves y=sin x and y=cos x meet when sin x=cos x⇔ tan x=1⇔ x=π4[0≤ x≤ π2]. Thus the point of intersection is (π4,(√ 2)2). We have (π4,(√ 2)2) and (π4,(√ 2)2), so the tangent lines at that point have slopes (√ 2)2 and - (√ 2)2....
The curves y=x^2 and y=x^3 meet when x^2=x^3⇔ x^3-x^2=0⇔ x^2(x-1)=0⇔ x=0, x=1. We have x=1 and x=1, so the tangent lines of both curves have slope 0 at x=0. Thus the angle between the curves is 0^(° ) at the point (0,0). For x=1, (0,0...
Find the area between the curves y=\sec^2(x) and y= \cos(x) in the interval -\pi/4 \leq x \leq \pi/4 Find the area between the curve of y = sin(\theta) and the \theta axis from \theta = \dfrac{\pi}{2} \; to \; \theta= \dfrac{3 \pi}{2...
Find the angle between the lines , (a^(2) - ab) y = (ab+b^(2))x+b^(3) , and (ab+b^(2)) y = (ab-a^2)x+a^(3) where a lt b lt 0
We we have two curves coming together, then the angle between the curves is the same as the angle between their tangent vectors. Answer and Explanation: Let {eq}\mathbf r(t)=\langle t\cos t,t\sin t,t \rangle {/eq} and {eq...
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Find the slope of the curve x=6t+3, y=2t2−7t at t=5. A) 13. B) 0. C) 6. D) 136.Slope:We have parametric equations that are quadratic and linear in nature. The slope of the curve at any point is the tangent of the angle that th...
geometry FindAngle find the angle between two lines or two circles Calling Sequence Parameters Description Examples Calling Sequence FindAngle( u , v ) Parameters u, v - two lines or circles Description The routine finds the angle between two lines u...
Find the area of the intersection of the circle r = sin θ and r = (1/{eq}\sqrt{3} {/eq}) cos θ. (Use symbolic notation and fractions where needed.) Area of a Polar Region: The area formed between polar curves {eq}r =...
FindAngle(l1, p1) FindAngle(A, T) Parameters l1, l2 - lines p1, p2 - planes s1, s2 - sphere A - a point T - a triangle Description • When two lines l1, l2 do not intersect, we define the angle determined by them as the angle between two lines through the or...