wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The tangent to the curve x = et cost, y = et sin t at t = π4 makes with x-axis an angle
(a) 0 (b) π4 (c) π3 (d) π2

Open in App
Solution


The given curve is x = et cost, y = et sint.

x = et cost

Differentiating both sides with respect to t, we get

dxdt=et×-sint+cost×et

dxdt=etcost-sint

y = et sint

Differentiating both sides with respect to t, we get

dydt=et×cost+sint×et

dydt=etcost+sint

Now,

Slope of tangent to the given curve =dydx=dydtdxdt=etcost+sintetcost-sint=cost+sintcost-sint

∴ Slope of tangent to the given curve at t=π4 =dydxt=π4 =cosπ4+sinπ4cosπ4-sinπ4=12+1212-12=20=

Let the angle made by the tangent to the given curve at t = π4 with the x-axis be θ.

∴ tanθ = Slope of tangent to the given curve at t=π4 =

tanθ=tanπ2

θ=π2


Thus, the tangent to the curve x = et cost, y = et sint at t = π4 makes with x-axis an angle π2.

Hence, the correct answer is option (d).

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Geometrical Interpretation of a Derivative
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon