מידע| זהויות בטריגנומטריה

[SIZE=4][B][U]זהויות של סינוס:[/U][/B][/SIZE]


[IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?%20sin%5Calpha%20%3D%20sin%28180-%5Calpha%29%20[/IMG]

[IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?%20sin%5Calpha%3D%20cos%2890-%5Calpha%29%20[/IMG]

[IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?%20sin%5Calpha%3Dtg%5Calpha%20%5Ccdot%20cos%5Calpha%20[/IMG]

[IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?sin%28-%5Calpha%29%3D-sin%20%5Calpha%20[/IMG]


[SIZE=4][B][U]זהויות של קוסינוס:[/U][/B][/SIZE]


[IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?%20-cos%5Calpha%20%3D%20cos%28180-%5Calpha%29%20[/IMG]

[IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?%20cos%5Calpha%3D%20sin%2890-%5Calpha%29%20[/IMG]

[IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?%20cos%5Calpha%3D%5Cfrac%7Bsin%5Calpha%7D%7Btg%5Calpha%7D%20[/IMG]

[IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?%20cos%28-%5Calpha%29%3Dcos%5Calpha%20[/IMG]


[CENTER][SIZE=4][B][U]זהויות של טגנגנס:[/U][/B][/SIZE]
[/CENTER]


[LEFT] [IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?tg%5Calpha%3D%5Cfrac%7Bsin%5Calpha%7D%7Bcos%5Calpha%7D%20[/IMG]

[IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?%20-tg%5Calpha%20%3D%20tg%28-%5Calpha%29%20[/IMG]

[IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?%20%20tg%2890-%5Calpha%29%20%3Dcot%5Calpha%3D%5Cfrac%7Bcos%5Calpha%7D%7Bsin%5Calpha%7D%20[/IMG]

[IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?%201%2Btg%5E2%5Calpha%3D%5Cfrac%7B1%7D%7Bcos%5E2%5Calpha%7D%20[/IMG]


[IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?tg%28%5Calpha%2B%5Cbeta%29%3D%5Cfrac%7Btan%5Calpha%2Btan%5Cbeta%7D%7B1-tg%5Calpha%5Ccdot%7Btg%5Cbeta%7D%7D[/IMG]




[CENTER][SIZE=4][B][U]זוויות מיוחדות:[/U][/B][/SIZE][/CENTER]
[RIGHT]
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[INDENT][LEFT] [IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?%0A%5Cbegin%7Bmatrix%7D%0A%5Csin%200%20%20%3D%20%20%5Csin%200%5E%5Ccirc%20%20%3D%20%200%20%20%3D%20%20%5Ccos%2090%5E%5Ccirc%20%20%20%3D%20%20%20%5Ccos%20%5Cleft%28%20%5Cfrac%20%7B%5Cpi%7D%20%7B2%7D%20%5Cright%29%20%20%3D%20%5Cfrac%7B%5Csqrt%7B0%7D%7D%7B2%7D%20%5C%5C%20%20%5C%5C%0A%5Csin%20%5Cleft%28%20%5Cfrac%7B%5Cpi%7D%7B6%7D%20%5Cright%29%20%20%3D%20%20%5Csin%2030%5E%5Ccirc%20%20%3D%20%201%2F2%20%20%3D%20%20%5Ccos%2060%5E%5Ccirc%20%3D%20%20%5Ccos%20%5Cleft%28%20%5Cfrac%20%7B%5Cpi%7D%7B3%7D%20%20%5Cright%29%20%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%20%5C%5C%20%20%5C%5C%0A%5Csin%20%5Cleft%28%20%5Cfrac%7B%5Cpi%7D%7B4%7D%20%5Cright%29%20%20%3D%20%20%5Csin%2045%5E%5Ccirc%20%20%3D%20%20%5Csqrt%7B2%7D%2F2%20%20%3D%20%20%5Ccos%2045%5E%5Ccirc%20%20%3D%20%20%5Ccos%20%5Cleft%28%20%5Cfrac%20%7B%5Cpi%7D%20%7B4%7D%20%5Cright%29%20%20%3D%20%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%20%20%5C%5C%20%20%5C%5C%0A%5Csin%20%5Cleft%28%5Cfrac%7B%5Cpi%7D%7B3%7D%5Cright%29%20%20%3D%20%5Csin%2060%5E%5Ccirc%20%20%3D%20%20%5Csqrt%7B3%7D%2F2%20%20%3D%20%5Ccos%2030%5E%5Ccirc%20%20%3D%20%20%5Ccos%20%5Cleft%28%20%5Cfrac%20%7B%5Cpi%7D%20%7B6%7D%20%5Cright%29%20%20%3D%20%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%20%20%5C%5C%20%20%5C%5C%0A%5Csin%20%5Cleft%28%5Cfrac%7B%5Cpi%7D%7B2%7D%20%5Cright%29%20%20%3D%20%20%5Csin%2090%5E%5Ccirc%20%20%3D%20%201%20%20%3D%20%20%5Ccos%200%5E%5Ccirc%20%20%3D%20%20%5Ccos%200%20%20%3D%20%5Cfrac%7B%5Csqrt%7B4%7D%7D%7B2%7D%0A%5Cend%7Bmatrix%7D%0A[/IMG]


[RIGHT]
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[/LEFT][/INDENT][RIGHT] [/RIGHT]
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[CENTER][SIZE=4][B][U]זהויות סכום והפרש זוויות:[/U][/B][/SIZE]

[IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?sin%20x%20%2B%20sin%20y%20%3D%202sin%28%5Cfrac%7Bx%20%2B%20y%7D%7B2%7D%29%20cos%28%5Cfrac%7Bx%20-%20y%7D%7B2%7D%29[/IMG]


[IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?sin%20x%20-%20sin%20y%20%3D%202cos%28%5Cfrac%7Bx%20%2B%20y%7D%7B2%7D%29%20sin%28%5Cfrac%7Bx%20-%20y%7D%7B2%7D%29[/IMG]


[IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?cos%20x%20%2B%20cos%20y%20%3D%202cos%28%5Cfrac%7Bx%20%2B%20y%7D%7B2%7D%29%20cos%28%5Cfrac%7Bx%20-%20y%7D%7B2%7D%29[/IMG]


[IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?cos%20x%20-%20cos%20y%20%3D%20-2sin%28%5Cfrac%7Bx%20%2B%20y%7D%7B2%7D%29%20sin%28%5Cfrac%7Bx%20-%20y%7D%7B2%7D%29[/IMG]


[SIZE=4][B][/B][/SIZE]
[SIZE=4][B][U]זהויות בסיסיות:[/U][/B][/SIZE]


[LEFT]
[IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?%20sin%5Calpha%3Dcos%2890-%5Calpha%29%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20sin%28180-%5Calpha%29%3Dsin%5Calpha%20[/IMG]

[IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?%20sin%5E2%5Calpha%2Bcos%5E2%5Calpha%3D1%20[/IMG]

[IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?%20cos%28-%5Calpha%29%3Dcos%5Calpha%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20cos%28180-%5Calpha%29%3D-cos%5Calpha[/IMG]

[IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?%20tan%5Calpha%3D%5Cfrac%7Bsin%5Calpha%7D%7Bcos%5Calpha%7D%20[/IMG]

[IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?%20sin2a%3D2sina%2Acosa%20[/IMG]


[IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?%20cos2x%3D2cos%5E2x-1%3D1-2sin%5E2x%3Dcos%5E2x-sin%5E2x%20[/IMG]




[CENTER][SIZE=4][B][U]זהויות מורכבות:[/U][/B][/SIZE]


[/CENTER]
[/LEFT]
[LEFT]
[IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?sin%28A%2BB%29%3Dsin%20A%20cos%20B%20%2B%20cos%20A%20sin%20B[/IMG]


[IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?sin%28A-B%29%3Dsin%20A%20cos%20B%20-%20cos%20A%20sin%20B[/IMG]


[IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?cos%28A%2BB%29%3Dcos%20A%20cos%20B%20-%20sin%20A%20sin%20B[/IMG]


[IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?cos%28A-B%29%3Dcos%20A%20cos%20B%20%2B%20sin%20A%20sin%20B[/IMG]


[IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?tg%28%5Calpha%2B%5Cbeta%29%3D%5Cfrac%7Btan%5Calpha%2Btan%5Cbeta%7D%7B1-tg%5Calpha%5Ccdot%7Btg%5Cbeta%7D%7D[/IMG]


[IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?%20cos%282A%29%3Dcos%5E2%28A%29-sin%5E2%28A%29%3D2cos%5E2%28A%29-1%3D1-2sin%5E2%28A%29%20[/IMG]




[CENTER][SIZE=4][B][U]זהויות כפל:[/U][/B][/SIZE]

[/CENTER]

[IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?sinAcosB%20%3D%20%5Cfrac%7Bsin%28A%20%2B%20B%29%2B%20sin%28A%20-%20B%29%7D%7B2%7D[/IMG]


[IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?cosAsinB%20%3D%20%5Cfrac%7Bsin%28A%20%2B%20B%29%20-%20sin%28A%20-%20B%29%7D%7B2%7D[/IMG]


[IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?cosAcosB%20%3D%20%5Cfrac%7Bcos%28A%20-%20B%29%20%2B%20cos%28A%20%2B%20B%29%7D%7B2%7D[/IMG]


[IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?sinAsinB%20%3D%20%5Cfrac%7Bcos%28A%20-%20B%29%20-%20cos%28A%20%2B%20B%29%7D%7B2%7D[/IMG]


[CENTER][SIZE=4][B][U]זהויות חיבור וחיסור:[/U][/B][/SIZE]

[/CENTER]
[LEFT]
[IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?sin%20x%20%2B%20sin%20y%20%3D%202sin%28%5Cfrac%7Bx%20%2B%20y%7D%7B2%7D%29%20cos%28%5Cfrac%7Bx%20-%20y%7D%7B2%7D%29[/IMG]


[IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?sin%20x%20-%20sin%20y%20%3D%202cos%28%5Cfrac%7Bx%20%2B%20y%7D%7B2%7D%29%20sin%28%5Cfrac%7Bx%20-%20y%7D%7B2%7D%29[/IMG]


[IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?cos%20x%20%2B%20cos%20y%20%3D%202cos%28%5Cfrac%7Bx%20%2B%20y%7D%7B2%7D%29%20cos%28%5Cfrac%7Bx%20-%20y%7D%7B2%7D%29[/IMG]


[IMG]http://www.emath.co.il/cgi-bin/mimetex.cgi?cos%20x%20-%20cos%20y%20%3D%20-2sin%28%5Cfrac%7Bx%20%2B%20y%7D%7B2%7D%29%20sin%28%5Cfrac%7Bx%20-%20y%7D%7B2%7D%29[/IMG]
[/LEFT]


[CENTER]
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