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شائع >

9.6=11.6cos(3.922t)

الحلّ

9.6 = 11.6 cos (3.922 t)

الحلّ

t = \frac{0.59600 \dots}{3.922} + \frac{2 πn}{3.922}, t = \frac{2 π}{3.922} - \frac{0.59600 \dots}{3.922} + \frac{2 πn}{3.922}

درجات

t = 8.70689 \dots^{\circ} + 91.78990 \dots^{\circ} n, t = 83.08301 \dots^{\circ} + 91.78990 \dots^{\circ} n

خطوات الحلّ

9.6 = 11.6 cos (3.922 t)

بدّل الأطراف

11.6 cos (3.922 t) = 9.6

10

اضرب الطرفين بـ

11.6 cos (3.922 t) = 9.6

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere is one digit to the right of the decimal point, therefore multiply by

10

11.6 cos (3.922 t) \cdot 10 = 9.6 \cdot 10

بسّط

116 cos (3.922 t) = 96

116 cos (3.922 t) = 96

116

اقسم الطرفين على

116 cos (3.922 t) = 96

116

اقسم الطرفين على

\frac{116 cos ( 3.922 t )}{116} = \frac{96}{116}

بسّط

cos (3.922 t) = \frac{24}{29}

cos (3.922 t) = \frac{24}{29}

Apply trig inverse properties

cos (3.922 t) = \frac{24}{29}

cos (3.922 t) = \frac{24}{29} :

حلول عامّة لـ

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

3.922 t = arccos (\frac{24}{29}) + 2 πn, 3.922 t = 2 π - arccos (\frac{24}{29}) + 2 πn

3.922 t = arccos (\frac{24}{29}) + 2 πn, 3.922 t = 2 π - arccos (\frac{24}{29}) + 2 πn

3.922 t = arccos (\frac{24}{29}) + 2 πn

حلّ:

t = \frac{arccos ( \frac{24}{29} )}{3.922} + \frac{2 πn}{3.922}

3.922 t = arccos (\frac{24}{29}) + 2 πn

3.922

اقسم الطرفين على

3.922 t = arccos (\frac{24}{29}) + 2 πn

3.922

اقسم الطرفين على

\frac{3.922 t}{3.922} = \frac{arccos ( \frac{24}{29} )}{3.922} + \frac{2 πn}{3.922}

بسّط

t = \frac{arccos ( \frac{24}{29} )}{3.922} + \frac{2 πn}{3.922}

t = \frac{arccos ( \frac{24}{29} )}{3.922} + \frac{2 πn}{3.922}

3.922 t = 2 π - arccos (\frac{24}{29}) + 2 πn

حلّ:

t = \frac{2 π}{3.922} - \frac{arccos ( \frac{24}{29} )}{3.922} + \frac{2 πn}{3.922}

3.922 t = 2 π - arccos (\frac{24}{29}) + 2 πn

3.922

اقسم الطرفين على

3.922 t = 2 π - arccos (\frac{24}{29}) + 2 πn

3.922

اقسم الطرفين على

\frac{3.922 t}{3.922} = \frac{2 π}{3.922} - \frac{arccos ( \frac{24}{29} )}{3.922} + \frac{2 πn}{3.922}

بسّط

t = \frac{2 π}{3.922} - \frac{arccos ( \frac{24}{29} )}{3.922} + \frac{2 πn}{3.922}

t = \frac{2 π}{3.922} - \frac{arccos ( \frac{24}{29} )}{3.922} + \frac{2 πn}{3.922}

t = \frac{arccos ( \frac{24}{29} )}{3.922} + \frac{2 πn}{3.922}, t = \frac{2 π}{3.922} - \frac{arccos ( \frac{24}{29} )}{3.922} + \frac{2 πn}{3.922}

أظهر الحلّ بالتمثيل العشريّ

t = \frac{0.59600 \dots}{3.922} + \frac{2 πn}{3.922}, t = \frac{2 π}{3.922} - \frac{0.59600 \dots}{3.922} + \frac{2 πn}{3.922}

رسم

أمثلة شائعة

2sin^2(x)=tan^2(x)

2 sin^{2} (x) = tan^{2} (x)

cos(θ)=0.5632

cos (θ) = 0.5632

sin(z)=-10

sin (z) = - 10

(sec^2(A)+cot^2(A))/(csc^2(A))=sec^2(A)

\frac{sec ^{2} ( A ) + cot ^{2} ( A )}{csc ^{2} ( A )} = sec^{2} (A)

cos^3(x)=-1

cos^{3} (x) = - 1