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شائع علم المثلثات >

solvefor t,0.08=0.1cos(4t)

الحلّ

solve for

t, 0.08 = 0.1 cos (4 t)

الحلّ

t = \frac{0.64350 \dots}{4} + \frac{πn}{2}, t = \frac{π}{2} - \frac{0.64350 \dots}{4} + \frac{πn}{2}

درجات

t = 9.21747 \dots^{\circ} + 9 0^{\circ} n, t = 80.78252 \dots^{\circ} + 9 0^{\circ} n

خطوات الحلّ

0.08 = 0.1 cos (4 t)

بدّل الأطراف

0.1 cos (4 t) = 0.08

100

اضرب الطرفين بـ

0.1 cos (4 t) = 0.08

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

2

digits to the right of the decimal point, therefore multiply by

100

0.1 cos (4 t) \cdot 100 = 0.08 \cdot 100

بسّط

10 cos (4 t) = 8

10 cos (4 t) = 8

10

اقسم الطرفين على

10 cos (4 t) = 8

10

اقسم الطرفين على

\frac{10 cos ( 4 t )}{10} = \frac{8}{10}

بسّط

cos (4 t) = \frac{4}{5}

cos (4 t) = \frac{4}{5}

Apply trig inverse properties

cos (4 t) = \frac{4}{5}

cos (4 t) = \frac{4}{5} :

حلول عامّة لـ

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

4 t = arccos (\frac{4}{5}) + 2 πn, 4 t = 2 π - arccos (\frac{4}{5}) + 2 πn

4 t = arccos (\frac{4}{5}) + 2 πn, 4 t = 2 π - arccos (\frac{4}{5}) + 2 πn

4 t = arccos (\frac{4}{5}) + 2 πn

حلّ:

t = \frac{arccos ( \frac{4}{5} )}{4} + \frac{πn}{2}

4 t = arccos (\frac{4}{5}) + 2 πn

4

اقسم الطرفين على

4 t = arccos (\frac{4}{5}) + 2 πn

4

اقسم الطرفين على

\frac{4 t}{4} = \frac{arccos ( \frac{4}{5} )}{4} + \frac{2 πn}{4}

بسّط

t = \frac{arccos ( \frac{4}{5} )}{4} + \frac{πn}{2}

t = \frac{arccos ( \frac{4}{5} )}{4} + \frac{πn}{2}

4 t = 2 π - arccos (\frac{4}{5}) + 2 πn

حلّ:

t = \frac{π}{2} - \frac{arccos ( \frac{4}{5} )}{4} + \frac{πn}{2}

4 t = 2 π - arccos (\frac{4}{5}) + 2 πn

4

اقسم الطرفين على

4 t = 2 π - arccos (\frac{4}{5}) + 2 πn

4

اقسم الطرفين على

\frac{4 t}{4} = \frac{2 π}{4} - \frac{arccos ( \frac{4}{5} )}{4} + \frac{2 πn}{4}

بسّط

\frac{4 t}{4} = \frac{2 π}{4} - \frac{arccos ( \frac{4}{5} )}{4} + \frac{2 πn}{4}

\frac{4 t}{4}

بسّط:

t

\frac{4 t}{4}

\frac{4}{4} = 1 :

اقسم الأعداد

= t

\frac{2 π}{4} - \frac{arccos ( \frac{4}{5} )}{4} + \frac{2 πn}{4}

بسّط:

\frac{π}{2} - \frac{arccos ( \frac{4}{5} )}{4} + \frac{πn}{2}

\frac{2 π}{4} - \frac{arccos ( \frac{4}{5} )}{4} + \frac{2 πn}{4}

\frac{2 π}{4}

اختزل:

\frac{π}{2}

\frac{2 π}{4}

2 :

إلغ العوامل المشتركة

= \frac{π}{2}

= \frac{π}{2} - \frac{arccos ( \frac{4}{5} )}{4} + \frac{2 πn}{4}

\frac{2 πn}{4}

اختزل:

\frac{πn}{2}

\frac{2 πn}{4}

2 :

إلغ العوامل المشتركة

= \frac{πn}{2}

= \frac{π}{2} - \frac{arccos ( \frac{4}{5} )}{4} + \frac{πn}{2}

t = \frac{π}{2} - \frac{arccos ( \frac{4}{5} )}{4} + \frac{πn}{2}

t = \frac{π}{2} - \frac{arccos ( \frac{4}{5} )}{4} + \frac{πn}{2}

t = \frac{π}{2} - \frac{arccos ( \frac{4}{5} )}{4} + \frac{πn}{2}

t = \frac{arccos ( \frac{4}{5} )}{4} + \frac{πn}{2}, t = \frac{π}{2} - \frac{arccos ( \frac{4}{5} )}{4} + \frac{πn}{2}

أظهر الحلّ بالتمثيل العشريّ

t = \frac{0.64350 \dots}{4} + \frac{πn}{2}, t = \frac{π}{2} - \frac{0.64350 \dots}{4} + \frac{πn}{2}

رسم

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