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  • Użytkownik Zadane
2013-07-15T21:00:44+02:00

1.

cosa = 0,8 = 8/10 = 4/5

 

sin²a + cos²a = 1

sin²a + (4/5)² = 1

sin²a = 1 - 16/25

sin²a = 9/25

sina = 3/5

 

tga = sina / cosa = 3/5 : 4/5 = 3/5 * 5/4 = 3/4

ctga = cosa / sina = 4/5 : 3/5 = 4/5 * 5/3 = 4/3

 

 

2.

cosa = 3/5

 

sin²a + cos²a = 1

sin²a + (3/5)² = 1

sin²a = 1 - 9/25

sin²a = 16/25

sina = 4/5

 

tga = sina / cosa = 4/5 : 3/5 = 4/5 * 5/3 = 4/3

ctga = cosa / sina = 3/5 : 4/5 = 3/5 * 5/4 = 3/4

 

3.

cosa = 3/2    <-----  coś nie tam, bo cosa nie moze takiej wartości posiadac

 

4.

ctga = 4/5

 

tga = 1 / ctga = 1 : 4/5 = 1 * 5/4 = 5/4

 

sina / cosa = tga

sina / cosa = 5/4

5cosa = 4sina

cosa = 4/5 sina

 

sin²a + cos²a = 1

sin²a + (4/5sina)² = 1

sin²a + 16/25sin²a = 1

41/25sin²a = 1

sin²a = 25/41

sina = 5/√41

sina = 5√41 / 41

 

cosa = 4/5 * 5√41 / 41

cosa = 4√41/ 41

2013-07-15T21:42:21+02:00

 

cosα = 0,8

sin²α + cos²α = 1

sin²α + 0,8² = 1

sin²α + 0,64 = 1

sin²α = 0,36

sinα = 0,6

 

tgα = sinα/cosα

 

tgα = 0,6/0,8 = 0,75

 

ctgα = 1/tgα

 

ctgα = 1/0,75 = 4/3

 

 

 

cosα = 3/5

9/25+ sin²α = 1

sin²α = 6/25

sinα = √6/5

 

tgα = √6/5 / 3/5 = √6/3

 

ctgα = 1/√6/3 = 3/√6 = 3√6/6 = √6/2

 

 

cosα = 3/2 - sprzeczność

 

ctgα = 4/5

 

tgα = 5/4

 

sinα/cosα = 5/4

5cosα = 4sinα => sinα = 5/4cosα

 

cos²α + 25/16cos²α = 1

41/16cos²α = 1

cos²α = 16/41

cosα = 4/√41 = 4√41/41

 

sinα = 5/4 * 4√41/41 = 5√41/41

 

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