Welcome to Mathsessential.com Concern & Answers Community. Ask any kind of math/science homework question and also obtain answers from various other members of the area.Q&A CategoriesBASIC MATH(93)PRE-ALGEBRA(441)ALGEBRA 1(2,216)GEOMETRY(864)ALGEBRA 2(2,745)TRIGONOMETRY(1,186)PRECALCULUS(1,903)CALCULUS(2,791)STATISTICS(129)PHYSICS(658)CHEMISTRY(136)MECHANICAL ENGINEERING(64)ELECTRICAL ENGINEERING(207)Winplot Tutorials(2)

Most renowned tagssolving-equationssystem-of-equationsfunctionsmathslope-intercept-formphysicshomework-helptrigonometric-identitiesintegrationsubstitution-methodlimitscalculus13,435 questions17,804 answers1,438 comments130,408 users

find an equation for the line tangent to curve at the suggest characterized by the provided worth of t 0 votes

x= 3 sin t, y= 3 cos t, t= 3pi/4.

You are watching: Find an equation for the line tangent to the curve at the point defined by the given value of t

equation-of-a-tangent-lineequation-of-a-lineaskedFeb 27, 2014in CALCULUSby andrewScholar

Please log in or register to include a comment. Please log in or register to answer this question. 1 Answer 0 votes

The parametric equation is *x* = 3 sin *t*,* y* = 3 cos *t*, *t* = 3π / 4.

When, *t* = 3π / 4, 3 *sin* (3π / 4) = 3(1 /√2) = 3 / √2.

When,* t* = 3π / 4, 3 *cos* (3π / 4) = 3(- 1 /√2) = - 3 / √2.

Because of this, the point is (3 / √2, - 3 / √2).

*dx* / *dt* = 3 *cos t*

*dy */ *dt* = 3 (- *sin t* ) = - 3 *sin t*

*dy* / *dx *= <*dy* / *dt* > / <*dx* / *dt* > = - 3 *sin t* / 3 *cos t* = -* tan t.*

When, *t* = 3π / 4, *dy* / *dx* = - *tan* (3π / 4) = - (- 1) = 1.

*y *" = 1.

This is the slope (*m *) of the tangent line to the implicit curve at (3 / √2, - 3 / √2).

To uncover the tangent line equation, substitute the values of *m* = 1 and (*x*, *y* ) = (3 / √2, - 3 / √2) in the slope intercept form of an equation.

*y* = *mx* + *b*

- 3 / √2 = 1(3 / √2) + *b*

*b = *- 3√2.

Substitute *m* = 1 and also *b = *- 3√2 in *y* = *mx* + *b.*

*y* = 1(*x *) - 3√2

*y* = *x* - 3√2.

See more: A Powerful Appetite Stimulator That Has Been Shown To Cause People To Hoard Food Is

The tangent line equation is** ***y* = *x* - 3√2.

answeredApr 10, 2014by lillyExpert Please log in or register to include a comment. Related questionsFind an equation of the tangent line to the curve at the given suggest. Y=sin(sinx) , (2pi,0)askedFeb 27, 2014in CALCULUSby dkinzApprenticeequation-of-a-tangent-linetangentequation-of-a-line given: y=arccos(4x) a)uncover the equation of the line tangent to the curve at x=1/8askedFeb 27, 2014in CALCULUSby paytonApprenticeequation-of-a-tangent-lineequation-of-a-linetangent create an equation of the line that is tangent to the circle at the given allude.x^2+y^2=24askedFeb 27, 2014in ALGEBRA 2by rockstarApprenticeequation-of-a-tangent-linetangent-of-a-circleequation-of-a-line Find an equation of the tangent line to the curve at the given point.askedJun 20, 2014in CALCULUSby anonymousequation-of-a-tangent-line discover the equation of the tangent line to the curve y=(2)/(1+e^-x) at the point (0,1)askedFeb 27, 2014in CALCULUSby futaiScholarequation-of-a-tangent-linetangent If the tangent line to y=f(x) at (9,−2) passes with the allude (5,9), then compute f(9).askedNov 28, 2013in ALGEBRA 1by dkinzApprenticeequation-of-a-lineequation-of-a-tangent-line Find an equation of the tangent lineaskedFeb 27, 2014in CALCULUSby angel12Scholarequation-of-a-tangent-lineequation-of-a-linetangent uncover the equation of the normal to the graph of the feature f(x)=-x^2+8x+4 at the point where x=-1askedFeb 27, 2014in CALCULUSby skylarApprenticeequation-of-a-tangent-linegraphing-functionsequation-of-a-line Find the slope of the tangent line to the provided polar curve at the allude speciﬁed by the value of θ.askedFeb 2, 2015in CALCULUSby anonymouspolar-equationsslope-of-the-tangent Find an equation of the tangent to the curve at the point corresponding to the provided worth of the parameter.askedFeb 2, 2015in CALCULUSby anonymousdifferentiationparametric-equationstangent Use Implicit Differentiation to discover equation of tangent line to ellipse 5x^2+xy+4y^2=40 at the allude (−2,−2)askedOct 27, 2017in CALCULUSby 1ndig0Rookiecalculusderivativesequation-of-a-tangent-lineimplicit-differentiationellipse discover the equation of the line tangent to the circle (x-1)^2+(y-1)^2=25 at the allude (4,-3)askedFeb 17, 2014in CALCULUSby paytonApprenticeequation-of-a-tangent-linecircles Find an equation of the tangent to the curve at the given allude by two methods:askedFeb 2, 2015in CALCULUSby anonymousdifferentiationparametric-equationstangent Find an equation of the tangent line to the curve at the provided point.askedJan 26, 2015in CALCULUSby anonymousequation-of-the-tangentdifferentiation Use implicit differentiation to find an equation of the tangent line to the curve at the given allude.askedJan 20, 2015in CALCULUSby anonymousimplicit-differentiation Find an equation of the tangent line to the curve at the given suggest.askedJan 20, 2015in CALCULUSby anonymoustangent-line Find an equation of the tangent line to the curve at the offered pointaskedJan 20, 2015in CALCULUSby anonymoustangent-line Find an equation of the tangent line to the curve at the offered suggest.askedJan 20, 2015in CALCULUSby anonymoustangent-line Find an equation of the tangent line to the curve at the provided pointaskedJan 13, 2015in CALCULUSby anonymoustangent-line Find values of x wright here tangent line to f(x)=(1/x) is parallel to the line y=-5x+9.askedFeb 27, 2014in CALCULUSby chrisgirlApprenticeequation-of-a-tangent-lineparallel-linesequation-of-a-line