2. Sketch the path and give a direction. r(t) = (2 cos t, 2 sin t), 0≤ t ≤ 2π r(t) = (e cos t, -3 sint), 0≤ t ≤ 2π r(t) = (4 cos t, 4 sint, t), 0≤ t ≤ 4T i) ii) iii)

Q: Solue the equation on the interval [o,27) a) cosla0) = - 42 %3D b.) 2 sin 2 x + 3 sin x = -1 C.) sin…

A: topic - trigonometric equations

Q: Suppose v. w = 6 and ||7× w|| = 4, and the angle between ỹ and w is 0. Find (a) tan 0 = (b) Ө —

A: v · w= |v| × |w| × cos(θ) =6 v × w = |v| |w| sin(θ) =4

Q: السؤال 3 -Sec2 (). dx tan (5). · dz O ). de tan tan . da O ). dz O tan

A:

Q: 7) T (u, ) -(υ, 2 cos u, 4sin u). Consider the parameterization With 0, y ve (1,3]. u € describing…

A: Direction of normal always positive y axis. So y component of the normal is positive.

Q: 12. Find tan(2r) if tan(x) = 2 (hint: use a double angle formula). ii) -3 iii) iv) not listed i) 4

A: We know that,  tan(2x)=2 tan(x)1-tan2(x) Given that, tanx=2 tan2x=221-22 tan2x=4-3

Q: 1) y = tan x 2) y = cot x 3) y = -tan x4) y = -cot x %3D A) B) C) D)

A:

Q: cos'p dp 3) 1- p?

A: Sol:Given ∫cos-1PdP1-P2     ....(1)now we have ,ddP Cos-1P = -11-P2 ...(2)from (1), u = cos-1P…

Q: If 0 is a first quadrant angle where P(u, v) = (-1, -2), tan 0: 5 + V5 - V5 5 - 5 - V5 5 + V5 5 - V5…

A:

Q: Q5: Find: a) £[3-5e²t + 4 sin t - 7 cos 3t] b) C- 3.s s²+16 5 s² +

A:

Q: 5. The coordinates of the points A, B and C, are (0, 1, 3), (-1, 0, 1) and (1, -1, 2) respectively.…

A:

Q: Use shifting graph to sketch a) y = 1-|V2 – 2x| b) y = 1- sin (0.5x)

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: 4 + 3 2. Ja x5 Find 2. dx + C

A:

Q: Given that = 4 and 6 ²|a²| 4 and = 3 and that = 3 and that (3 — 5) à is perpendicular to (à + 26).…

A: Given: a→=4    and     b→=33a→-b→ is perpendicular to a→+2b→.

Q: Q33) Use shifting graph to sketch a) y+1 = |-3+ v2x| b) y = 2 + cos (0.1x)

A: The function translation  or transformation rules: If  y=f(x)+b then the graph shifts the function…

Q: tane de sece 4 Q10 3 7 a) 2-2 b) (2 1) c) 24-2 d) (2 -1) 1/3 1/5 5/4

A:

Q: c) h(p,g,0) = psin@cose ah sin@cos0 ; ah = pcos@cose answer: - %3D ah =-p sinøsin0 d) W(P,V,8,v.g)=…

A:

Q: 3) ft)= (t+リ sin (t+z)= t sinけtz) + sint +2) Asin(よ)+ - Cole) ds s Sin(2) +1- Gd ニ (8+1) - sind -…

A: We have to find the Laplace transformation of f(t).

Q: OQ =r = 10 and Q (-6; y) Determine: a) y b) sin 0 c) d) tan 0 Cos e Q(-6; y)

A: We will use distance formula and polar co-ordinates to solve this

Q: 3T/4 18) 3 sec 0 tan 0 de

A:

Q: O sec sec 0 – 3 = tan 0 – 4

A:

Q: g) u = x³ + 3x²y

A:

Q: 1. Express as a sum or difference a.) sin 7t sin t b.) cos 6u cos (-4u) c.) cos 2t sin 6t d.) 2…

A:

Q: c) 25 sin? x – 9 = 0 d) (5 cos x + 2)(2 sin x – 1) = 0 True of false?

A: So , solving these trigonometric equations in [0,2pi]