1. a) Substitute u = sin(x) to evaluate sin^2(x) cos^3(x) dx. [trig identity sin2(x)+cos2(x) = 1]....
Find the solutions for cos(2?)=3−sin2(?)−5cos(?)−cos2(?)cos(2x)=3−sin2(x)−5cos(x)−cos2(x), in the interval [0,2?).[0,2π). The answer(s) is/are ?= 5.5 Solutions of Trig Equations: Problem 17 Previous Problem Problem List Next Problem (1 point) Find the solutions for cos(2x) = 3 – sin?(x) - 5 cos(x) - cos(x), in the interval [0, 21). The answer(s) is/are x = Note: If there is more than one solution enter them separated by commas. If needed enter a as pi.
EXAMPLE 2 Find sin$(7x) cos”7x) dx. SOLUTION We could convert cos?(7x) to 1 - sin?(7x), but we would be left with an expression in terms of sin(7x) with no extra cos(7x) factor. Instead, we separate a single sine factor and rewrite the remaining sin" (7x) factor in terms of cos(7x): sin'(7x) cos”(7x) = (sinº(7x))2 cos(7x) sin(7x) = (1 - Cos?(7x))2 cos?(7x) sin(7x). in (7x) cos?(7x) and ich is which? Substituting u = cos(7x), we have du = -sin (3x) X...
QUESTION 3 Evaluate the integral by using multiple substitutions. SV1 1 + sin2 (x-7) sin (x-7) cos (x-7) dx o 3 (1+ sinº x) (1 + sin? x)3/2 + c 3 O AV1 + sin?(x - 7) +C og (1 + sin? (x - 7)) 3/2 + c O (1 + cos2 (x - 7) 3/2 + c
(a) Use the complex exponential to prove the double angle formula cos2 -sin2 a cos(2.ar) . (b) Use the complex exponential to evaluate the indefinite integral sin(4t) dt. (a) Use the complex exponential to prove the double angle formula cos2 -sin2 a cos(2.ar) . (b) Use the complex exponential to evaluate the indefinite integral sin(4t) dt.
(3) Evaluate the indefinite integral. ſtan(x) + cos2 (2) dx cos(2)
Tutorial Exercise Evaluate the integral using the substitution rule. sin(x) 1/3 1* dx cos(x) Step 1 of 4 To integrate using substitution, choose u to be some function in the integrand whose derivative (or some constant multiple of whose derivative) is a factor of the integrand. Rewriting a quotient as a product can help to identify u and its derivative. 70/3 1." sin(x) dx = L" (cos(x) since) dx cos?(X) Notice that do (cos(x)) = and this derivative is a...
cos(x)-sin*(x) Verify the identity: cos2(x) (Hint: try factoring) = 1- tan?(x)
sin^2(theta/2)/sin^2 Complete the identity. sin sin2 = ? sinde O e cos? 2 1 4- cos e O_1 2cos e O sin? 2 + 2 cos e
13 pts) Let R be the relation on R deÖned by xRy means "sin2 (x) + cos2 (y) = 1". Recall the Pythagorean identity: 8u 2 R we have sin2 (u) + cos2 (u) = 1. (a) (9 pts) PROVE that R is an equivalence relation on R. (b) (4 pts) Describe all elements of the (inÖnite) equivalence class [0]. Recall: sin(0) = 0 and cos(0) = 1. 2. (13 pts) Let R be the relation on R defined by...
Consider the following surface parametrization. x-5 cos(8) sin(φ), y-3 sin(θ) sin(p), z-cos(p) Find an expression for a unit vector, n, normal to the surface at the image of a point (u, v) for θ in [0, 2T] and φ in [0, π] -3 cos(θ) sin(φ), 5 sin(θ) sin(φ),-15 cos(q) 16 sin2(0) sin2(p)216 cos2(p)9 3 cos(9) sin(9),-5 sin(θ) sin(9), 15 cos(q) 16 sin2(0) sin2(p)216 cos2(p)9 v 16 sin2(0) sin2@c 216 cos2@t9(3 cos(θ) sin(φ), 5 sin(θ) sin(φ) , 15 cos(q) 216 cos(φ)...