6. (4 points each) Evaluate the following trigonometric values. Show your work. (a.) (135) (d.) sin(-3)
Use the trigonometric function values of the quadrantal angles to evaluate. 6 sin 0° +5 sin 270° 6 sin 0° +5 sin 270° (Simplify your answer. Type an integer or a fraction.)
5. (24 points) Evaluate each of the following. Show your work. (e) $1,1x) dx (f) sin(1+1) e* cos(1 – e*) dx (€) Set (ing) dt (h) 1,2 cos(x) cos(sin(x)) dx
9. (5 points each) Evaluate each of the following. Show all of your work and give exact answers. If the answer is a number, do not round. de = ez dr = () (4 + 2) di
3. Use the trigonometric substitution r = a sin(0) to evaluate the following indefinite integral: da
4. Evaluate the following integrals using the Residue Theorem. Justify your calculations, show the work. (10 points each) a) 12 cos a + 13 2 da b) (x2 +6x + 10)2 x sin 2x 24 13 da: c)
4. Evaluate the following integrals using the Residue Theorem. Justify your calculations, show the work. (10 points each) a) 12 cos a + 13 2 da b) (x2 +6x + 10)2 x sin 2x 24 13 da: c)
Use your calculator to find the values of the following trigonometric function to four decimal places. [8 pts.] Hint: Your calculator should be in radian mode. (radian) a. sin38° b. cos21° c. tan32.7° d. sin 200° e. sin 6 p f. tan 4 p 5 g. cos ( p /18) h. sin 3 p/10
Evaluate the following integral using Integration by Parts or Trigonometric Substitution dc Show all your work: i.e. If you use Integration by Parts, clearly define u,du, v, dv or if you use Trig Sub clearly define what substitution you use for I as well as dr and other corresponding parts of your substitution
Evaluate the following integral using Integration by Parts or Trigonometric Substitution dc Show all your work: i.e. If you use Integration by Parts, clearly define u,du, v, dv or if you use Trig Sub clearly define what substitution you use for I as well as dr and other corresponding parts of your substitution
2. (20 points) Evaluate the following integral using Integration by Parts or Trigonometric Substitution dr Show all your work: i.e. If you use Integration by Parts, clearly define u,du, v, dv or if you use Trig Sub clearly define what substitution you use for r as well as dr and other corresponding parts of your substitution
4. We would like to evaluate d de sin(t)2tdt (a) (6 points) Compute | (x) = f', sin(t)2tdt (b) (6 points) Find f'(x). (c) (6 points) State the fundamental theorem of calculus. (d) (6 points) Use the fundamental theorem of calculus to compute ź (S-, sin(t2)2tdt) without first computing the integral.