The tangent to the curve given by x = e t . cost, y = e t . sint at t =
π/4 makes with x-axis an angle:
(A)0
(B) π/4
(C) π/3
(D) π/2



Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
NCERT Exemplar - MCQs
Question 2 Important
Question 3 Important You are here
Question 4 Important
Question 5 Important
Question 6
Question 7 Important
Question 8 Important
Question 9 Important
Question 10
Question 11 Important
Question 12 Important
Question 13
Question 14
Question 15 Important
Question 16 Important
Question 17 Important
Question 1 Important Deleted for CBSE Board 2024 Exams
Question 2 Deleted for CBSE Board 2024 Exams
Question 3 Important Deleted for CBSE Board 2024 Exams You are here
Question 4 Deleted for CBSE Board 2024 Exams
Question 5 Deleted for CBSE Board 2024 Exams
Question 6 Deleted for CBSE Board 2024 Exams
Question 7 Important Deleted for CBSE Board 2024 Exams
Question 8 Deleted for CBSE Board 2024 Exams
Question 9 Important Deleted for CBSE Board 2024 Exams
Question 10 Important Deleted for CBSE Board 2024 Exams
Question 11 Deleted for CBSE Board 2024 Exams
Question 12 Deleted for CBSE Board 2024 Exams
Question 13 Deleted for CBSE Board 2024 Exams
Last updated at May 29, 2023 by Teachoo
Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Question 3 The tangent to the curve given by x = et . cost, y = et . sint at t = 𝜋/4 makes with x-axis an angle: 0 (B) 𝜋/4 (C) 𝜋/3 (D) 𝜋/2 Given curve 𝒙=𝒆^𝒕.𝒄𝒐𝒔𝒕 and 𝒚=𝒆^𝒕.𝒔𝒊𝒏𝒕 Finding slope of tangent 𝒅𝒚/𝒅𝒙=(𝒅𝒚/𝒅𝒕)/(𝒅𝒙/𝒅𝒕) 𝒙=𝒆^𝒕.𝒄𝒐𝒔𝒕 Differentiating 𝑥 𝑤.𝑟.𝑡 𝑡 𝑑𝑥/𝑑𝑡=𝑒^𝑡 𝑐𝑜𝑠𝑡−𝑒^𝑡 𝑠𝑖𝑛𝑡 𝒅𝒙/𝒅𝒕=𝑒^𝑡 (𝑐𝑜𝑠𝑡−𝑠𝑖𝑛𝑡) 𝒚=𝒆^𝒕.𝒔𝒊𝒏𝒕 Differentiating y 𝑤.𝑟.𝑡 𝑑𝑦/𝑑𝑡=𝑒^𝑡 𝑠𝑖𝑛𝑡+𝑒^𝑡 𝑐𝑜𝑠𝑡 𝒅𝒚/𝒅𝒕=𝑒^𝑡 (𝑠𝑖𝑛𝑡\+𝑐𝑜𝑠𝑡) Now, 𝒅𝒚/𝒅𝒙=(𝒅𝒚/𝒅𝒕)/(𝒅𝒙/𝒅𝒕) 𝑑𝑦/𝑑𝑥=(𝑒^𝑡 (𝑠𝑖𝑛𝑡\+𝑐𝑜𝑠𝑡)" " )/(𝑒^𝑡 (𝑐𝑜𝑠𝑡−𝑠𝑖𝑛𝑡)" " ) 𝑑𝑦/𝑑𝑥=( (𝒔𝒊𝒏𝒕\+𝒄𝒐𝒔𝒕)" " )/( (𝒄𝒐𝒔𝒕−𝒔𝒊𝒏𝒕)" " ) Putting 𝐭=𝛑/𝟒 ├ 𝒅𝒚/𝒅𝒙┤|_(𝒕=𝝅/𝟒)=( (𝑠𝑖𝑛 𝜋/4 \+ 𝑐𝑜𝑠 𝜋/4)" " )/( (𝑐𝑜𝑠 𝜋/4 − 𝑠𝑖𝑛 𝜋/4)" " ) = (1/√2+1/√2)/(1/√2−1/√2) = (2/(√2))/0 = ∞ Let 𝜽 be the angle made by tangent with the 𝑥- axis. Slope = 𝐭𝐚𝐧𝜽 ∞ = tan𝜃 tan〖𝜃=∞〗 ∴ 𝜽= 𝝅/𝟐 So, the correct answer is (D)