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شائع علم المثلثات >

4^{1/3}sec(x)=4(1/(4^{1/3)})csc(x)

الحلّ

4^{\frac{1}{3}} sec (x) = 4 (\frac{1}{4 ^{\frac{1}{3}}}) csc (x)

الحلّ

x = 1.00863 \dots + πn

درجات

x = 57.79069 \dots^{\circ} + 18 0^{\circ} n

خطوات الحلّ

4^{\frac{1}{3}} sec (x) = 4 (\frac{1}{4 ^{\frac{1}{3}}}) csc (x)

من الطرفين

4 \frac{1}{4 ^{\frac{1}{3}}} csc (x)

اطرح

4^{\frac{1}{3}} sec (x) - 4^{\frac{2}{3}} csc (x) = 0

sin, cos :

عبّر بواسطة

4^{\frac{1}{3}} sec (x) - 4^{\frac{2}{3}} csc (x)

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

:Use the basic trigonometric identity

= 4^{\frac{1}{3}} \cdot \frac{1}{cos ( x )} - 4^{\frac{2}{3}} csc (x)

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

:Use the basic trigonometric identity

= 4^{\frac{1}{3}} \cdot \frac{1}{cos ( x )} - 4^{\frac{2}{3}} \cdot \frac{1}{sin ( x )}

4^{\frac{1}{3}} \cdot \frac{1}{cos ( x )} - 4^{\frac{2}{3}} \cdot \frac{1}{sin ( x )}

بسّط:

\frac{4 ^{\frac{1}{3}} sin ( x ) - 4 ^{\frac{2}{3}} cos ( x )}{cos ( x ) sin ( x )}

4^{\frac{1}{3}} \cdot \frac{1}{cos ( x )} - 4^{\frac{2}{3}} \cdot \frac{1}{sin ( x )}

4^{\frac{1}{3}} \cdot \frac{1}{cos ( x )} = \frac{4 ^{\frac{1}{3}}}{cos ( x )}

4^{\frac{1}{3}} \cdot \frac{1}{cos ( x )}

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

:اضرب كسور

= \frac{1 \cdot 4 ^{\frac{1}{3}}}{cos ( x )}

1 \cdot 4^{\frac{1}{3}} = 4^{\frac{1}{3}} :

اضرب

= \frac{4 ^{\frac{1}{3}}}{cos ( x )}

4^{\frac{2}{3}} \cdot \frac{1}{sin ( x )} = \frac{4 ^{\frac{2}{3}}}{sin ( x )}

4^{\frac{2}{3}} \cdot \frac{1}{sin ( x )}

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

:اضرب كسور

= \frac{1 \cdot 4 ^{\frac{2}{3}}}{sin ( x )}

1 \cdot 4^{\frac{2}{3}} = 4^{\frac{2}{3}} :

اضرب

= \frac{4 ^{\frac{2}{3}}}{sin ( x )}

= \frac{4 ^{\frac{1}{3}}}{cos ( x )} - \frac{4 ^{\frac{2}{3}}}{sin ( x )}

cos (x), sin (x)

المضاعف المشترك الأصغر لـ:

cos (x) sin (x)

cos (x), sin (x)

Lowest Common Multiplier (LCM)

Compute an expression comprised of factors that appear either in

cos (x)

sin (x)

= cos (x) sin (x)

اكتب مجددًا الكسور بحيث يكون المقام مشترك

cos (x) sin (x)

اضرب كل بسط ومقام بتعبير الذي يؤدّي إلى مقام مشترك

For

\frac{4 ^{\frac{1}{3}}}{cos ( x )} :

multiply the denominator and numerator by

sin (x)

\frac{4 ^{\frac{1}{3}}}{cos ( x )} = \frac{4 ^{\frac{1}{3}} sin ( x )}{cos ( x ) sin ( x )}

For

\frac{4 ^{\frac{2}{3}}}{sin ( x )} :

multiply the denominator and numerator by

cos (x)

\frac{4 ^{\frac{2}{3}}}{sin ( x )} = \frac{4 ^{\frac{2}{3}} cos ( x )}{sin ( x ) cos ( x )}

= \frac{4 ^{\frac{1}{3}} sin ( x )}{cos ( x ) sin ( x )} - \frac{4 ^{\frac{2}{3}} cos ( x )}{sin ( x ) cos ( x )}

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

:بما أنّ المقامات متساوية، اجمع البسوط

= \frac{4 ^{\frac{1}{3}} sin ( x ) - 4 ^{\frac{2}{3}} cos ( x )}{cos ( x ) sin ( x )}

= \frac{4 ^{\frac{1}{3}} sin ( x ) - 4 ^{\frac{2}{3}} cos ( x )}{cos ( x ) sin ( x )}

\frac{4 ^{\frac{1}{3}} sin ( x ) - 4 ^{\frac{2}{3}} cos ( x )}{cos ( x ) sin ( x )} = 0

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

4^{\frac{1}{3}} sin (x) - 4^{\frac{2}{3}} cos (x) = 0

Rewrite using trig identities

4^{\frac{1}{3}} sin (x) - 4^{\frac{2}{3}} cos (x) = 0

cos (x) \neq = 0, cos (x)

اقسم الطرفين على

\frac{4 ^{\frac{1}{3}} sin ( x ) - 4 ^{\frac{2}{3}} cos ( x )}{cos ( x )} = \frac{0}{cos ( x )}

بسّط

\frac{4 ^{\frac{1}{3}} sin ( x )}{cos ( x )} - 4^{\frac{2}{3}} = 0

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

:Use the basic trigonometric identity

4^{\frac{1}{3}} tan (x) - 4^{\frac{2}{3}} = 0

4^{\frac{1}{3}} tan (x) - 4^{\frac{2}{3}} = 0

انقل

4^{\frac{2}{3}}

إلى الجانب الأيمن

4^{\frac{1}{3}} tan (x) - 4^{\frac{2}{3}} = 0

للطرفين

4^{\frac{2}{3}}

أضف

4^{\frac{1}{3}} tan (x) - 4^{\frac{2}{3}} + 4^{\frac{2}{3}} = 0 + 4^{\frac{2}{3}}

بسّط

4^{\frac{1}{3}} tan (x) = 4^{\frac{2}{3}}

4^{\frac{1}{3}} tan (x) = 4^{\frac{2}{3}}

4^{\frac{1}{3}}

اقسم الطرفين على

4^{\frac{1}{3}} tan (x) = 4^{\frac{2}{3}}

4^{\frac{1}{3}}

اقسم الطرفين على

\frac{4 ^{\frac{1}{3}} tan ( x )}{4 ^{\frac{1}{3}}} = \frac{4 ^{\frac{2}{3}}}{4 ^{\frac{1}{3}}}

بسّط

\frac{4 ^{\frac{1}{3}} tan ( x )}{4 ^{\frac{1}{3}}} = \frac{4 ^{\frac{2}{3}}}{4 ^{\frac{1}{3}}}

\frac{4 ^{\frac{1}{3}} tan ( x )}{4 ^{\frac{1}{3}}}

بسّط:

tan (x)

\frac{4 ^{\frac{1}{3}} tan ( x )}{4 ^{\frac{1}{3}}}

4^{\frac{1}{3}} :

إلغ العوامل المشتركة

= tan (x)

\frac{4 ^{\frac{2}{3}}}{4 ^{\frac{1}{3}}}

بسّط:

4^{\frac{1}{3}}

\frac{4 ^{\frac{2}{3}}}{4 ^{\frac{1}{3}}}

\frac{x ^{a}}{x ^{b}} = x^{a - b}

:فعّل قانون القوى

\frac{4 ^{\frac{2}{3}}}{4 ^{\frac{1}{3}}} = 4^{\frac{2}{3} - \frac{1}{3}}

= 4^{\frac{2}{3} - \frac{1}{3}}

\frac{2}{3} - \frac{1}{3} = \frac{1}{3} :

اطرح الأعداد

= 4^{\frac{1}{3}}

tan (x) = 4^{\frac{1}{3}}

tan (x) = 4^{\frac{1}{3}}

tan (x) = 4^{\frac{1}{3}}

Apply trig inverse properties

tan (x) = 4^{\frac{1}{3}}

tan (x) = 4^{\frac{1}{3}} :

حلول عامّة لـ

tan (x) = a \Rightarrow x = arctan (a) + πn

x = arctan (4^{\frac{1}{3}}) + πn

x = arctan (4^{\frac{1}{3}}) + πn

أظهر الحلّ بالتمثيل العشريّ

x = 1.00863 \dots + πn

رسم

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