Instituto Superior de Engenharia de Coimbra
Licenciatura em Engenharia Mecˆanica
An´alise Matem´atica I
Solu¸c˜oes - Notas Te´oricas
Exerc´ıcios - Fun¸c˜oes trigonom´etricas
1. (a) −1/2
(b) √2/2
(c) 1
(d) 2
(e) −√3/3
2. sin(a) = √24/5
3. (a) x= 2kπ ∨x=π/3+2kπ/3, com k∈Z
(b) x=±5π/18 + 2kπ/3, com k∈Z
(c) x=kπ ∨x=±π/3+2kπ, com k∈Z
Exerc´ıcios - Fun¸c˜oes trigonom´etricas inversas
1. (a) arcsin(1/2) = π/6
(b) arctan(−√3) = −π/3
(c) π/2 + arccos(√2/2) = 3π/4
(d) cos(arctan(3/4)) = 4/5
2. cos(arcsin(2x)) = √1−4x2
3. —
Exerc´ıcios - Fun¸c˜oes exponenciais e logar´ıtmicas
1. (a) e−ln(4) = 1/4;
(b) log3(1
27 ) = −3
2. x= 0
3. x > e
Exerc´ıcios - Fun¸c˜oes hiperb´olicas
1. (a) cosh(0) = 1
(b) sinh(ln(2)) = 3/4
(c) sec(1) = 2e/(e2+ 1)
(d) coth(ln(5)) = 26/24
2. —
3. cosh(x) = √13/2
Patr´ıcia Santos, 2014/2015 1
