InStructor. Linda Houston Student: Jimi Ogletree Course: MATH 2124 Analytical Ge

Question

InStructor. Linda Houston Student: Jimi Ogletree Course: MATH 2124 Analytical Geometry Assignment: Section 11.2 Homework Date: 7/24/16 and Calculus II d y Find an equation for the line tangent to the curve at the point defined by the given value of t. Also, find the value of at dx this point. x F sint, y cos t, t Write the equation of the tangent line X (Type exact answers, using radicals as needed.) d y What is the value of at this point? dx d y (Type an exact answer, using radicals as needed.) dx Instructor: Linda Houston Student: Jimi Ogletree Course: MATH 2124 Analytical Geometry Assignment: Section 11.2 Homework Date: 7/24/16 and Calculus II d y Find an equation for the line tangent to the curve at the point defined by the given value of t. Also, find the value of at dx this point. x sec t- 1, ECOS tit Write the equation of the tangent line 3 3 9 3 X 16 16 (Type exact answers, using radicals as needed.) What is the value of at this point? dy 3 3 d x dy2 32 (Type an exact answer, using radicals as needed.)

Explanation / Answer

x = sin t
dx/dt = cos t

y = cos t
dy/dt = - sin t

dy/dx = (dy/dt) / (dx/dt) = -sin t / cos t = -tan t
at t = -pi/4 ,
dy/dx = -tan (-pi/4) = 1
y = sin (pi/4) = 1/sqrt(2)
x = cos (pi/4) = 1/sqrt(2)

so tangent will be:
y-yo = slope * (x-xo)
(y-1/sqrt(2)) = 1 * (x- 1/sqrt (2))
y=x
Answer:
y= x is the equation of tangent

I am allowed to answer only 1 question at a time

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