Lista de exercícios do ensino médio para impressão

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(FEI - 1977) Calcular $\phantom{X}c\phantom{X}$, sabendo que:
$\,a\,=\,4\,$
$\,b\,=\,3\sqrt{\,2\,}\,$
$\,\hat{C}\,=\,45^o\,$
triângulo escaleno

 



resposta: $\,c\,=\,\sqrt{10}\,m\,$
×
a)
Simplificar a expressão $\phantom{X}cos\left(\dfrac{\,3\pi\,}{\,2\,}\,+\,x\right)\phantom{X}$
b)
Calcular $\phantom{X}sen^2\left(\dfrac{\,3\pi\,}{\,2\,}\,+\,x\right) + cos^2\left(\dfrac{\,3\pi\,}{\,2\,}\,+\,x\right)\phantom{X}$
c)
Calcular $\phantom{X}cos^2\left(\dfrac{\,3\pi\,}{\,2\,}\,+\,x\right) + cos^2\,x\phantom{X}$

 



resposta: a)$\,sen\,x\,$ b)1 c)1
×
a)
Simplificar a expressão $\phantom{X}sen\left(\dfrac{\,3\pi\,}{\,2\,}\,+\,x\right)\phantom{X}$
b)
Calcular $\phantom{X}sen^2\left(\dfrac{\,3\pi\,}{\,2\,}\,+\,x\right) + cos^2\left(\dfrac{\,3\pi\,}{\,2\,}\,+\,x\right)\phantom{X}$
c)
Calcular $\phantom{X}sen^2\,x\,+\,sen^2\left(\dfrac{\,3\pi\,}{\,2\,}\,+\,x\right)\phantom{X}$

 



resposta: a)$\,-cos\,x\,$ b)1 c)1
×
a)
Simplificar a expressão $\phantom{X}cos\left(\dfrac{\,3\pi\,}{\,2\,}\,-\,x\right)\phantom{X}$
b)
Calcular $\phantom{X}sen^2\left(\dfrac{\,3\pi\,}{\,2\,}\,-\,x\right) + cos^2\left(\dfrac{\,3\pi\,}{\,2\,}\,-\,x\right)\phantom{X}$
c)
Calcular $\phantom{X}sen^2\,x\,+\,sen^2\left(\dfrac{\,3\pi\,}{\,2\,}\,-\,x\right)\phantom{X}$

 



resposta: a)$\,-cos\,x\,$ b)1 c)1
×
a)
Simplificar a expressão $\phantom{X}cos\left(\dfrac{\,3\pi\,}{\,2\,}\,-\,x\right)\phantom{X}$
b)
Calcular $\phantom{X}sen^2\left(\dfrac{\,3\pi\,}{\,2\,}\,-\,x\right) + cos^2\left(\dfrac{\,3\pi\,}{\,2\,}\,-\,x\right)\phantom{X}$
c)
Calcular $\phantom{X}cos^2\left(\dfrac{\,3\pi\,}{\,2\,}\,-\,x\right)\,+\,cos^2\,x\phantom{X}$

 



resposta: a)$\,-sen\,x\,$ b)1 c)1
×
(PUCRJ - 2018) Simplificando a expressão $\phantom{X}2\,\centerdot\,\dfrac{\,(3^6\,+\,3^5)\,}{\,3^4\,-\,3^3\,}\phantom{X}$
a)
12
b)
13
c)
3
d)
36
e)
1

 



resposta: (D)
×
a)
Simplificar a expressão $\phantom{X}sen\,(\frac{\,\pi\,}{\,2\,}\,+\,x)\phantom{X}$
b)
Calcular $\phantom{X}sen^2\,\frac{\,4\pi\,}{\,9\,}\,+\,cos^2\,\frac{\,4\pi\,}{\,9\,}\phantom{X}$
c)
Calcular $\phantom{X}sen^2\,\frac{\,4\pi\,}{\,9\,}\,+\,cos^2\,\frac{\,5\pi\,}{\,9\,}\phantom{X}$
d)
Calcular $\phantom{X}\frac{\,\pi\,}{\,2\,}\,-\,\frac{\,4\pi\,}{\,9\,}\phantom{X}$
e)
Calcular $\phantom{X}\frac{\,5\pi\,}{\,9\,}\,-\,\frac{\,\pi\,}{\,2\,}\phantom{X}$
f)
Calcular $\phantom{X}sen^2\,\frac{\,4\pi\,}{\,9\,}\,+\,sen^2\,\frac{\,\pi\,}{\,18\,}\phantom{X}$
g)
Calcular $\phantom{X}sen^2\,\frac{\,5\pi\,}{\,9\,}\,+\,sen^2\,\frac{\,\pi\,}{\,18\,}\phantom{X}$

 



resposta: a)$\,cos x\,$b)1c)1d)$\,\frac{\pi}{18}\,$e)$\,\frac{\pi}{18}\,$f)1g)1
×
(VUNESP) A expressão $\phantom{X}\dfrac{\,cos^2\,\theta\,}{\;1\,-\,sen\,\theta}\phantom{X}$, com $\,sen\,\theta\,\ne\,1\,$, é igual a:
a)
$\,sen\,\theta\,$
b)
$\,sen\,\theta\,+\,1\,$
c)
$\,tg\,\theta\,\centerdot\,cos\,\theta\,$
d)
$\,1\,$
e)
$\,\frac{\,sen\,\theta\,}{\,sec\,\theta\,}\,$

 



resposta: (B)
×
Sabendo que $\,sen x - cos x = a\,$, calcule:
a)$\,sen\,x\,\centerdot\,cos\,x\,$
b)$\,sen^3\,x\,-\,cos^3\,x\,$

 



resposta: a)$\,\dfrac{1\,-\,a^2}{2}\,$
b)$\,\dfrac{3a\,-\,a^3}{2}\,$
×
Sabe-se que $\,sen\,\dfrac{\,4\pi\,}{\,9\,}\,=\,a\,$
a)
Qual o sinal de $\,a\,$? Justifique.
b)
Calcule, em função de $\,a\,$, $\,sen\,\dfrac{\,5\pi\,}{\,9\,}\,$.
c)
Calcule $\,sen\,\dfrac{\,\pi\,}{\,18\,}\;$ e $\;cos\,\dfrac{\,\pi\,}{\,18\,}\;$

 



resposta: a) positivo porque o arco $\,\frac{4\pi}{9}\,$ pertence ao primeiro quadrante $\,0\,\lt\,\frac{4\pi}{9}\,\lt\,\frac{\pi}{2}\,$
b)$\,a\,$
c)$\,sen\frac{\pi}{18}\,=\,\sqrt{1\,-\,a^2}\,$ e $\,cos\frac{\pi}{18}\,=\,a\,$
×
Calcule o valor de
a) $\,sen^2\,70^o\,+\,cos^2\,100^o\,$
b) $\,sen^2\,55^o\,+\,cos^2\,55^o\,$

 



resposta: a)1 b)1
×
Para quais valores de $\,x\,$ temos $\,tg\,x\,=\,\sqrt{\,3\,}\,$

 



resposta: $\,x\,=\,\frac{\;\pi\;}{3}\,+\,k\pi,\,k\,\in\,\mathbb{Z}\,$
×
Sabendo que $\phantom{X}tg\,x\,=\,3\phantom{X}$, $\phantom{X}\pi\,\lt\,x\,\lt\,\frac{\,3\pi\,}{\,2\,}\,$, calcule $\,sen\,x\;-\;cos\,x\,$.

 



resposta: $\,-\frac{\sqrt{10\,}}{5}\,$
×
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