If the angle made by the tangent at the point (x0, y0) on the curve x=12(t+ sin t cos t), y =12(1+ sin t )2, 0

Question

If the angle made by the tangent at the point (x0, y0) on the curve x=12(t+ sin t cos t), y =12(1+ sin t )2, 0< t <(π/2), with the positive x-axis is (π/3), then y 0 is equal to (A) 6(3+2 √2) (B) 3(7+4 √3) (C) 27 (D) 48

Tardigrade Admin · Accepted Answer

(d y/d x)=(2(1+ sin t) × cos t/1+ cos 2 t) ⇒ (2(1+ sin t) cos t/2 cos 2 t)=√3 ⇒ t=(π/6), y0=27

Q. If the angle made by the tangent at the point $(x_{0}, y_{0})$ on the curve $x = 12 (t + sin t cos t)$ , $y = 12 (1 + sin t)^{2}, 0 < t < \frac{π}{2}$ , with the positive $x$ -axis is $\frac{π}{3}$ , then $y_{0}$ is equal to

$6 (3 + 22)$

$3 (7 + 43)$

$27$

$48$

$\frac{d y}{d x} = \frac{2 ( 1 + s i n t ) \times c o s t}{1 + c o s 2 t}$
$\Rightarrow \frac{2 ( 1 + s i n t ) c o s t}{2 c o s ^{2} t} = 3$
$\Rightarrow t = \frac{π}{6}, y_{0} = 27$

Q. If the angle made by the tangent at the point (x0​,y0​) on the curve x=12(t+sintcost), y=12(1+sint)2,0<t<2π​, with the positive x-axis is 3π​, then y0​ is equal to

6(3+22​)

3(7+43​)

27

48