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شائع علم المثلثات >

sqrt(11)sin(x+37.09)=1

الحلّ

11 sin (x + 37.0 9^{\circ}) = 1

الحلّ

x = 0.30627 \dots + 36 0^{\circ} n - 37.08999 \dots^{\circ}, x = 18 0^{\circ} - 0.30627 \dots + 36 0^{\circ} n - 37.08999 \dots^{\circ}

+1

راديان

x = 0.30627 \dots - \frac{245 π}{1189} + 2 πn, x = π - 0.30627 \dots - \frac{245 π}{1189} + 2 πn

خطوات الحلّ

11 sin (x + 37.0 9^{\circ}) = 1

11

اقسم الطرفين على

11 sin (x + 37.08999 \dots^{\circ}) = 1

11

اقسم الطرفين على

\frac{11 sin ( x + 37.08999 \dots ^{\circ} )}{11} = \frac{1}{11}

بسّط

\frac{11 sin ( x + 37.08999 \dots ^{\circ} )}{11} = \frac{1}{11}

\frac{11 sin ( x + 37.08999 \dots ^{\circ} )}{11}

بسّط:

sin (x + 37.08999 \dots^{\circ})

\frac{11 sin ( x + 37.08999 \dots ^{\circ} )}{11}

11 :

إلغ العوامل المشتركة

= sin (x + 37.08999 \dots^{\circ})

\frac{1}{11}

بسّط:

\frac{11}{11}

\frac{1}{11}

\frac{11}{11}

اضرب بالمرافق

= \frac{1 \cdot 11}{11 11}

1 \cdot 11 = 11

1111 = 11

1111

a a = a

:فعْل قانون الجذور

1111 = 11

= 11

= \frac{11}{11}

sin (x + 37.08999 \dots^{\circ}) = \frac{11}{11}

sin (x + 37.08999 \dots^{\circ}) = \frac{11}{11}

sin (x + 37.08999 \dots^{\circ}) = \frac{11}{11}

Apply trig inverse properties

sin (x + 37.08999 \dots^{\circ}) = \frac{11}{11}

sin (x + 37.08999 \dots^{\circ}) = \frac{11}{11} :

حلول عامّة لـ

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

x + 37.08999 \dots^{\circ} = arcsin (\frac{11}{11}) + 36 0^{\circ} n, x + 37.08999 \dots^{\circ} = 18 0^{\circ} - arcsin (\frac{11}{11}) + 36 0^{\circ} n

x + 37.08999 \dots^{\circ} = arcsin (\frac{11}{11}) + 36 0^{\circ} n, x + 37.08999 \dots^{\circ} = 18 0^{\circ} - arcsin (\frac{11}{11}) + 36 0^{\circ} n

x + 37.08999 \dots^{\circ} = arcsin (\frac{11}{11}) + 36 0^{\circ} n

حلّ:

x = arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}

x + 37.08999 \dots^{\circ} = arcsin (\frac{11}{11}) + 36 0^{\circ} n

arcsin (\frac{11}{11}) + 36 0^{\circ} n

بسّط:

arcsin (\frac{1}{11}) + 36 0^{\circ} n

arcsin (\frac{11}{11}) + 36 0^{\circ} n

\frac{11}{11} = \frac{1}{11}

\frac{11}{11}

n a = a^{\frac{1}{n}}

:فعْل قانون الجذور

11 = 1 1^{\frac{1}{2}}

= \frac{1 1 ^{\frac{1}{2}}}{11}

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

:فعّل قانون القوى

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

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

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

اطرح الأعداد

= \frac{1}{1 1 ^{\frac{1}{2}}}

a^{\frac{1}{n}} = n a

:فعْل قانون الجذور

1 1^{\frac{1}{2}} = 11

= \frac{1}{11}

= arcsin (\frac{1}{11}) + 36 0^{\circ} n

x + 37.08999 \dots^{\circ} = arcsin (\frac{1}{11}) + 36 0^{\circ} n

انقل

37.08999 \dots^{\circ}

إلى الجانب الأيمن

x + 37.08999 \dots^{\circ} = arcsin (\frac{1}{11}) + 36 0^{\circ} n

من الطرفين

37.08999 \dots^{\circ}

اطرح

x + 37.08999 \dots^{\circ} - 37.08999 \dots^{\circ} = arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}

بسّط

x = arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}

x = arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}

x + 37.08999 \dots^{\circ} = 18 0^{\circ} - arcsin (\frac{11}{11}) + 36 0^{\circ} n

حلّ:

x = 18 0^{\circ} - arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}

x + 37.08999 \dots^{\circ} = 18 0^{\circ} - arcsin (\frac{11}{11}) + 36 0^{\circ} n

18 0^{\circ} - arcsin (\frac{11}{11}) + 36 0^{\circ} n

بسّط:

18 0^{\circ} - arcsin (\frac{1}{11}) + 36 0^{\circ} n

18 0^{\circ} - arcsin (\frac{11}{11}) + 36 0^{\circ} n

\frac{11}{11} = \frac{1}{11}

\frac{11}{11}

n a = a^{\frac{1}{n}}

:فعْل قانون الجذور

11 = 1 1^{\frac{1}{2}}

= \frac{1 1 ^{\frac{1}{2}}}{11}

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

:فعّل قانون القوى

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

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

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

اطرح الأعداد

= \frac{1}{1 1 ^{\frac{1}{2}}}

a^{\frac{1}{n}} = n a

:فعْل قانون الجذور

1 1^{\frac{1}{2}} = 11

= \frac{1}{11}

= 18 0^{\circ} - arcsin (\frac{1}{11}) + 36 0^{\circ} n

x + 37.08999 \dots^{\circ} = 18 0^{\circ} - arcsin (\frac{1}{11}) + 36 0^{\circ} n

انقل

37.08999 \dots^{\circ}

إلى الجانب الأيمن

x + 37.08999 \dots^{\circ} = 18 0^{\circ} - arcsin (\frac{1}{11}) + 36 0^{\circ} n

من الطرفين

37.08999 \dots^{\circ}

اطرح

x + 37.08999 \dots^{\circ} - 37.08999 \dots^{\circ} = 18 0^{\circ} - arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}

بسّط

x = 18 0^{\circ} - arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}

x = 18 0^{\circ} - arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}

x = arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}, x = 18 0^{\circ} - arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}

أظهر الحلّ بالتمثيل العشريّ

x = 0.30627 \dots + 36 0^{\circ} n - 37.08999 \dots^{\circ}, x = 18 0^{\circ} - 0.30627 \dots + 36 0^{\circ} n - 37.08999 \dots^{\circ}

رسم

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