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شائع علم المثلثات >

solvefor t,cos(wt+k)=(20)/((2pif)^2)

الحلّ

solve for

t, cos (wt + k) = \frac{20}{( 2 \cdot π \cdot f ) ^{2}}

الحلّ

t = \frac{arccos ( \frac{5}{π ^{2} f ^{2}} )}{w} + \frac{2 πn}{w} - \frac{k}{w}, t = - \frac{arccos ( \frac{5}{π ^{2} f ^{2}} )}{w} + \frac{2 πn}{w} - \frac{k}{w}

+1

راديان

t = \frac{arccos ( \frac{5}{π ^{2} f ^{2}} )}{w} - \frac{k}{w} + \frac{2 π}{w} n, t = - \frac{arccos ( \frac{5}{π ^{2} f ^{2}} )}{w} - \frac{k}{w} + \frac{2 π}{w} n

خطوات الحلّ

cos (wt + k) = \frac{20}{( 2 π f ) ^{2}}

\frac{20}{( 2 π f ) ^{2}}

بسّط:

\frac{5}{π ^{2} f ^{2}}

\frac{20}{( 2 π f ) ^{2}}

(2 π f)^{2} = 2^{2} π^{2} f^{2}

(2 π f)^{2}

(a \cdot b)^{n} = a^{n} b^{n}

:فعّل قانون القوى

= 2^{2} π^{2} f^{2}

= \frac{20}{2 ^{2} π ^{2} f ^{2}}

20

حلل إلى عوامل:

2^{2} \cdot 5

20 = 2^{2} \cdot 5

حلّل إلى عوامل

= \frac{2 ^{2} \cdot 5}{2 ^{2} π ^{2} f ^{2}}

2^{2} :

إلغ العوامل المشتركة

= \frac{5}{π ^{2} f ^{2}}

Apply trig inverse properties

cos (wt + k) = \frac{5}{π ^{2} f ^{2}}

cos (wt + k) = \frac{5}{π ^{2} f ^{2}} :

حلول عامّة لـ

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

wt + k = arccos (\frac{5}{π ^{2} f ^{2}}) + 2 πn, wt + k = - arccos (\frac{5}{π ^{2} f ^{2}}) + 2 πn

wt + k = arccos (\frac{5}{π ^{2} f ^{2}}) + 2 πn, wt + k = - arccos (\frac{5}{π ^{2} f ^{2}}) + 2 πn

wt + k = arccos (\frac{5}{π ^{2} f ^{2}}) + 2 πn

حلّ:

t = \frac{arccos ( \frac{5}{π ^{2} f ^{2}} )}{w} + \frac{2 πn}{w} - \frac{k}{w}; w \neq = 0

wt + k = arccos (\frac{5}{π ^{2} f ^{2}}) + 2 πn

انقل

k

إلى الجانب الأيمن

wt + k = arccos (\frac{5}{π ^{2} f ^{2}}) + 2 πn

من الطرفين

k

اطرح

wt + k - k = arccos (\frac{5}{π ^{2} f ^{2}}) + 2 πn - k

بسّط

wt = arccos (\frac{5}{π ^{2} f ^{2}}) + 2 πn - k

wt = arccos (\frac{5}{π ^{2} f ^{2}}) + 2 πn - k

w; w \neq = 0

اقسم الطرفين على

wt = arccos (\frac{5}{π ^{2} f ^{2}}) + 2 πn - k

w; w \neq = 0

اقسم الطرفين على

\frac{wt}{w} = \frac{arccos ( \frac{5}{π ^{2} f ^{2}} )}{w} + \frac{2 πn}{w} - \frac{k}{w}; w \neq = 0

بسّط

t = \frac{arccos ( \frac{5}{π ^{2} f ^{2}} )}{w} + \frac{2 πn}{w} - \frac{k}{w}; w \neq = 0

t = \frac{arccos ( \frac{5}{π ^{2} f ^{2}} )}{w} + \frac{2 πn}{w} - \frac{k}{w}; w \neq = 0

wt + k = - arccos (\frac{5}{π ^{2} f ^{2}}) + 2 πn

حلّ:

t = - \frac{arccos ( \frac{5}{π ^{2} f ^{2}} )}{w} + \frac{2 πn}{w} - \frac{k}{w}; w \neq = 0

wt + k = - arccos (\frac{5}{π ^{2} f ^{2}}) + 2 πn

انقل

k

إلى الجانب الأيمن

wt + k = - arccos (\frac{5}{π ^{2} f ^{2}}) + 2 πn

من الطرفين

k

اطرح

wt + k - k = - arccos (\frac{5}{π ^{2} f ^{2}}) + 2 πn - k

بسّط

wt = - arccos (\frac{5}{π ^{2} f ^{2}}) + 2 πn - k

wt = - arccos (\frac{5}{π ^{2} f ^{2}}) + 2 πn - k

w; w \neq = 0

اقسم الطرفين على

wt = - arccos (\frac{5}{π ^{2} f ^{2}}) + 2 πn - k

w; w \neq = 0

اقسم الطرفين على

\frac{wt}{w} = - \frac{arccos ( \frac{5}{π ^{2} f ^{2}} )}{w} + \frac{2 πn}{w} - \frac{k}{w}; w \neq = 0

بسّط

t = - \frac{arccos ( \frac{5}{π ^{2} f ^{2}} )}{w} + \frac{2 πn}{w} - \frac{k}{w}; w \neq = 0

t = - \frac{arccos ( \frac{5}{π ^{2} f ^{2}} )}{w} + \frac{2 πn}{w} - \frac{k}{w}; w \neq = 0

t = \frac{arccos ( \frac{5}{π ^{2} f ^{2}} )}{w} + \frac{2 πn}{w} - \frac{k}{w}, t = - \frac{arccos ( \frac{5}{π ^{2} f ^{2}} )}{w} + \frac{2 πn}{w} - \frac{k}{w}

رسم

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