Odpowiedzi

2011-08-20T20:38:48+02:00

cos α = 0,8

sin²α + cos² α  = 1

sin² α + 0,64=1

sin² α = 0,36

sin α =0,6

 

tg α = sin α / cos α = 0,6 / 0,8 = 0,75

 

ctg α = 4/3

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sin α = 0,4

sin²α + cos² α  = 1

0,16+cos² α = 1

0,84 = cos² α

cos² α = 21/25

cos α = √21 / 5

 

tg α = 0,4 / (√21 / 5)= 0,4* 5/√21=2/√21 = 2√21 / 21

ctg α = √21 / 2

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tg α = 2,4

ctg α = 1 / 2,4 = 1 / (12/5) = 1 * 5/12 = 5/12

 

2,4 = sin α / cos α

sin α =2,4 cos α

 

sin² α + cos² α = 1

(2,4cos α)² + cos² α = 1

5,76 cos² α + cos² α = 1

6,76 cos² α = 1

169/25 cos² α = 1

cos ² α = 25/169

cos α = 5/13

 

sin α = 12/5  *  5/13 = 12 * 1/13=12/13

 

2011-08-20T21:26:33+02:00

1. cosα= 0,8

x^{2}+8^{2}=10^{2} \\x^{2}+64=100\\ x^{2}=36\\ x=6

sin\alpha=\frac{6}{10}=0,6\\ tg \alpha=\frac{6}{8}=0,75\\ ctg\alpha=\frac{8}{6}=1\frac{1}{3}

 

2. sinα=0,4

x^{2}+4^{2}=10^{2}\\ x^{2}+16=100\\ x^{2}=84\\ x=\sqrt{84}=\sqrt{4 \cdot 21}=2\sqrt{21}

cos\alpha=\frac{2\sqrt{21}}{10}=\frac{\sqrt{21}}{5}\\ tg\alpha=\frac{4}{2\sqrt{21}}=\frac{2}{\sqrt{21}}\cdot \frac{\sqrt{21}}{\sqrt{21}}=\frac{2\sqrt{21}}{21}\\ ctg\alpha=\frac{2\sqrt{21}}{4}=\frac{\sqrt{21}}{2}

 

3. tg\alpha=2,4=\frac{12}{5}

5^{2}+12^{2}=x^{2}\\ x^{2}=25+144\\ x^{2}=169\\ x=13

sin\alpha=\frac{12}{13}\\ cos \alpha=\frac{5}{13}\\ ctg\alpha=\frac{5}{12}