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פּוֹפּוּלָרִי טריגונומטריה >

csc^2(x)=(1/(cos(x)))^2

פתרון

csc^{2} (x) = (\frac{1}{cos ( x )})^{2}

פתרון

x = \frac{3 π}{4} + πn, x = \frac{π}{4} + πn

מעלות

x = 13 5^{\circ} + 18 0^{\circ} n, x = 4 5^{\circ} + 18 0^{\circ} n

צעדי פתרון

csc^{2} (x) = (\frac{1}{cos ( x )})^{2}

משני האגפים

(\frac{1}{cos ( x )})^{2}

החסר

csc^{2} (x) - \frac{1}{cos ^{2} ( x )} = 0

csc^{2} (x) - \frac{1}{cos ^{2} ( x )}

פשט את:

\frac{csc ^{2} ( x ) cos ^{2} ( x ) - 1}{cos ^{2} ( x )}

csc^{2} (x) - \frac{1}{cos ^{2} ( x )}

csc^{2} (x) = \frac{csc ^{2} ( x ) cos ^{2} ( x )}{cos ^{2} ( x )}

:המר את המספרים לשברים

= \frac{csc ^{2} ( x ) cos ^{2} ( x )}{cos ^{2} ( x )} - \frac{1}{cos ^{2} ( x )}

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

:מאחר והמכנים שווים, חבר את המונים

= \frac{csc ^{2} ( x ) cos ^{2} ( x ) - 1}{cos ^{2} ( x )}

\frac{csc ^{2} ( x ) cos ^{2} ( x ) - 1}{cos ^{2} ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

csc^{2} (x) cos^{2} (x) - 1 = 0

csc^{2} (x) cos^{2} (x) - 1

פרק לגורמים את:

(cos (x) csc (x) + 1) (cos (x) csc (x) - 1)

csc^{2} (x) cos^{2} (x) - 1

a^{m} b^{m} = (ab)^{m}

:הפעל את חוק החזקות

cos^{2} (x) csc^{2} (x) = (cos (x) csc (x))^{2}

= (cos (x) csc (x))^{2} - 1

x^{2} - y^{2} = (x + y) (x - y)

הפעל את חוק הפרש הריבועים

(cos (x) csc (x))^{2} - 1 = (cos (x) csc (x) + 1) (cos (x) csc (x) - 1)

= (cos (x) csc (x) + 1) (cos (x) csc (x) - 1)

(cos (x) csc (x) + 1) (cos (x) csc (x) - 1) = 0

פתור כל חלק בנפרד

cos (x) csc (x) + 1 = 0 or cos (x) csc (x) - 1 = 0

cos (x) csc (x) + 1 = 0 : x = \frac{3 π}{4} + πn

cos (x) csc (x) + 1 = 0

Rewrite using trig identities

cos (x) csc (x) + 1

csc (x) cos (x) = cot (x)

csc (x) cos (x)

sin, cos :

בטא באמצאות

csc (x) cos (x)

csc (x) = \frac{1}{sin ( x )}

:Use the basic trigonometric identity

= \frac{1}{sin ( x )} cos (x)

\frac{1}{sin ( x )} cos (x)

פשט את:

\frac{cos ( x )}{sin ( x )}

\frac{1}{sin ( x )} cos (x)

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

:הכפל שברים

= \frac{1 cos ( x )}{sin ( x )}

1 \cdot cos (x) = cos (x) :

הכפל

= \frac{cos ( x )}{sin ( x )}

= \frac{cos ( x )}{sin ( x )}

= \frac{cos ( x )}{sin ( x )}

\frac{cos ( x )}{sin ( x )} = cot (x)

:Use the basic trigonometric identity

= cot (x)

= 1 + cot (x)

1 + cot (x) = 0

לצד ימין

1

העבר

1 + cot (x) = 0

משני האגפים

1

החסר

1 + cot (x) - 1 = 0 - 1

פשט

cot (x) = - 1

cot (x) = - 1

cot (x) = - 1 :

פתרונות כלליים עבור

cot (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

x = \frac{3 π}{4} + πn

x = \frac{3 π}{4} + πn

cos (x) csc (x) - 1 = 0 : x = \frac{π}{4} + πn

cos (x) csc (x) - 1 = 0

Rewrite using trig identities

cos (x) csc (x) - 1

csc (x) cos (x) = cot (x)

csc (x) cos (x)

sin, cos :

בטא באמצאות

csc (x) cos (x)

csc (x) = \frac{1}{sin ( x )}

:Use the basic trigonometric identity

= \frac{1}{sin ( x )} cos (x)

\frac{1}{sin ( x )} cos (x)

פשט את:

\frac{cos ( x )}{sin ( x )}

\frac{1}{sin ( x )} cos (x)

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

:הכפל שברים

= \frac{1 cos ( x )}{sin ( x )}

1 \cdot cos (x) = cos (x) :

הכפל

= \frac{cos ( x )}{sin ( x )}

= \frac{cos ( x )}{sin ( x )}

= \frac{cos ( x )}{sin ( x )}

\frac{cos ( x )}{sin ( x )} = cot (x)

:Use the basic trigonometric identity

= cot (x)

= - 1 + cot (x)

- 1 + cot (x) = 0

לצד ימין

1

העבר

- 1 + cot (x) = 0

לשני האגפים

1

הוסף

- 1 + cot (x) + 1 = 0 + 1

פשט

cot (x) = 1

cot (x) = 1

cot (x) = 1 :

פתרונות כלליים עבור

cot (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

x = \frac{π}{4} + πn

x = \frac{π}{4} + πn

אחד את הפתרונות

x = \frac{3 π}{4} + πn, x = \frac{π}{4} + πn

גרף

דוגמאות פופולריות