Question

E7 (b și c)
E8
va rog, dau coroana
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Answer 1

Răspuns:

Explicație pas cu pas:

7b) sinx  = √((1-(cosx)^2)

sinx = -+√(1 -16/25) = -+√(9/25) = -+3/5

Cum x in (3*pi/2, 2*pi),   sinx = -3/5

tgx = sinx/cosx = -3/5*5/4 = -3/4

ctgx = 1/tgx = -4/3

c) cosx/sinx = 5/12

5cosx =12sinx

5√(1-sin^2) = 12sinx

25(1 -sin^2) = 144sin^2

144sin^2 +25sin^2 =25

169sin^2 = 25,  sin^2 = 25/169

sinx = -+ 5/13

Cum x in (3*pi/2, 2*pi),   sinx = -5/13

cosx = √((1 -sin^2) = √(1 - 25/169)

cosx = -+√(144/169) = -12/13

Cum x in (3*pi/2, 2*pi),  cosx = 12/13

8) sinx +√(1-sin^2) = -√2

√(1-sin^2) = -√2 -sinx

1 - sin^2 = 2 +2√2sinx + sin^2

2sin^2 +2√2sinx +1 = 0

(√2sinx +1)^2 = 0

√2sinx = -1,  sinx = -√2/2

cosx = √(1-sin^2) = √(1 -2/4)

cosx = √(1/2) = √2/2

Cum x in (pi, 3*pi/2),   cosx = -√2/2

tgx = sinx/cosx,   ctgx = 1/tgx

etc.