Question

1- Determine o valor do seno, cosseno e tangente de cada arco:
a) 135°
b) 300°
c) 315°
d) 120°
e) 210°
f) 150°

2- Verdadeiro ou Falso:
a) sen 45° = sen 225°
b) sen 45° = sen 135°
c) sen pi/3 = -sen (-pi/3)
d) cos 30° = cos 150°
e) cos 150° = sen 150°

Answer 1

1- Determine o valor do seno, cosseno e tangente de cada arco:

a)

$\mathsf{sen(135^{\circ})=sen(45^{\circ})=\dfrac{\sqrt{2}}{2}}$

$\mathsf{cos(135^{\circ})=-cos(45^{\circ})=-\dfrac{\sqrt{2}}{2}}$

$\mathsf{tg(135^{\circ})=-tg(45^{\circ})=-1}$

b)

$\mathsf{c</p><p>sen(300^{\circ})=-sen(60^{\circ})=-\dfrac{\sqrt{3}}{2}}$

$\mathsf{cos(300^{\circ})=cos(60^{\circ})=-</p><p>\dfrac{1}{2}}$

$\mathsf{tg(300^{\circ})=-tg(60^{\circ})=-\sqrt{3}}$

c)

$\mathsf{sen(315^{\circ})=-sen(45^{\circ})=-\dfrac{\sqrt{2}}{2}}$

$\mathsf{cos(315^{\circ})=cos(45^{\circ})=\dfrac{\sqrt{2}}{2}}$

$\mathsf{tg(315^{\circ})=-tg(45^{\circ})=-1}$

d) 120°

$\mathsf{sen(120^{\circ})=sen(60^{\circ})=\dfrac{\sqrt{3}}{2}}$

$\mathsf{cos(120^{\circ})=-cos(60^{\circ})=-\dfrac{1}{2}}$

$\mathsf{tg(120^{\circ})=-tg(60^{\circ})=-\sqrt{3}}$

e)

$\mathsf{sen(210^{\circ})=-sen(30^{\circ})=-\dfrac{1}{2}}$

$\mathsf{cos(210^{\circ})=-cos(30^{\circ})=-\dfrac{\sqrt{3}}{2}}$

$\mathsf{tg(210^{\circ})=tg(30^{\circ})=\dfrac{\sqrt{3}}{3}}$

f) 150°

$\mathsf{sen(150^{\circ})=sen(10^{\circ})=\dfrac{1}{2}}$

$\mathsf{cos(150^{\circ})=-cos(30^{\circ})=-\dfrac{\sqrt{3}}{2}}$

2- Verdadeiro ou Falso:

a) sen 45° = sen 225° F

b) sen 45° = sen 135°✅

c) sen pi/3 = -sen (-pi/3) ✅

d) cos 30° = cos 150°F

e) cos 150° = sen 150°F

Answer 2

Explicação passo-a-passo:

1- Determine o valor do seno, cosseno e tangente de cada arco:

a) 135°

$\boxed{ \boxed{sen \: 45 = \frac{ \sqrt{2} }{2} }} \\ \boxed{ \boxed{ - cos \: 45 = - \frac{ \sqrt{2} }{2} }} \\ \boxed{ \boxed{ tang \: 45 = 1 }}$

b) 300°

$\boxed{ \boxed{ - sen \: 60 = - \frac{ \sqrt{3} }{2} }} \\ \boxed{ \boxed{ cos \: 60 = \frac{1}{2} }} \\ \boxed{ \boxed{ - Tang 60= - \sqrt{3} }}$

c) 315°

$\boxed{ \boxed{ - sen \: 45 = - \frac{ \sqrt{2} }{2} }} \\ \boxed{ \boxed{ cos \: 45 = \frac{ \sqrt{2} }{2} }} \\ \boxed{ \boxed{ - tang \: 45 = - 1}}$

d) 120°

$\boxed{ \boxed{ sen \: 60 = \frac{ \sqrt{3} }{2} }} \\ \boxed{ \boxed{ - cos \:60 = - \frac{1}{2} }} \\ \boxed{ \boxed{ - tang \: 60 = - \sqrt{3} }}$

e) 210°

$\boxed{ \boxed{ - sen \: 30 = - \frac{1}{2} }} \\ \boxed{ \boxed{ - cos \: 30 = - \frac{ \sqrt{3} }{2} }} \\ \boxed{ \boxed{ tang \: 30 = \frac{ \sqrt{3} }{3} }}$

f) 150°

$\boxed{ \boxed{ sen \: 30 = \frac{1}{2} }} \\ \boxed{ \boxed{ - cos \: 30 = - \frac{ \sqrt{3} }{2} }} \\ \boxed{ \boxed{ - tang \: 30 = - \frac{ \sqrt{3} }{3} }}$

2- Verdadeiro ou Falso:

a) sen 45° = sen 225°

Falso

b) sen 45° = sen 135°

verdadeiro

c) sen pi/3 = -sen (-pi/3)

verdadeiro

d) cos 30° = cos 150°

Falso

e) cos 150° = sen 150°

falso