University:
San Diego State University
Course:
MATH 151 | Calculus II
Academic year:

2023
Views:

489

Pages:

1
Author:

Carly Preston

Workshop #9 1. The number ONE identity in trigonometry is the Pythagorean Identity, which says cos2 x+sin2 x = 1. Divide both sides of the equation by cos2 x. After simplifying, what new identity do you get? Z 2. Consider the integral tan x sec2 x dx. (a) Explain why u = tan x is a possibly useful substitution. (b) Use this substitution to compute the integral. Z 3. Consider the integral tan x sec4 x dx. Use the substitution u = tan x to compute this integral. 4. Compute the following integrals. Z tan x sin2 x dx (a) Z cos5 x √ (b) dx sin x Z (c) tan3 x dx Z (d) tan x sin2 x dx 5. The double angle identity for cosine is cos(2x) = cos2 x − sin2 x. (a) Using the Pythagorean Identity, replace cos2 x with 1 − sin2 x. Then solve this new equation for sin2 x. Z (b) Use what you did above to compute sin4 x dx.