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شائع علم المثلثات >

solvefor t,v=100cos(50t+20)v

الحلّ

solve for

t, v = 100 cos (50 t + 2 0^{\circ}) v

الحلّ

t = \frac{18 0 ^{\circ} n}{25} - 0. 4^{\circ} + \frac{1.56079 \dots}{50}, t = 7. 2^{\circ} - 0. 4^{\circ} + \frac{18 0 ^{\circ} n}{25} - \frac{1.56079 \dots}{50}

راديان

t = - \frac{π}{450} + \frac{1.56079 \dots}{50} + \frac{π}{25} n, t = \frac{π}{25} - \frac{π}{450} - \frac{1.56079 \dots}{50} + \frac{π}{25} n

خطوات الحلّ

v = 100 cos (50 t + 2 0^{\circ}) v

بدّل الأطراف

100 cos (50 t + \frac{π}{9}) v = v

100 v; v \neq = 0

اقسم الطرفين على

100 cos (50 t + \frac{π}{9}) v = v

100 v; v \neq = 0

اقسم الطرفين على

\frac{100 cos ( 50 t + \frac{π}{9} ) v}{100 v} = \frac{v}{100 v}; v \neq = 0

بسّط

cos (50 t + \frac{π}{9}) = \frac{1}{100}; v \neq = 0

cos (50 t + \frac{π}{9}) = \frac{1}{100}; v \neq = 0

Apply trig inverse properties

cos (50 t + 2 0^{\circ}) = \frac{1}{100}

cos (50 t + 2 0^{\circ}) = \frac{1}{100} :

حلول عامّة لـ

cos (x) = a \Rightarrow x = arccos (a) + 36 0^{\circ} n, x = 36 0^{\circ} - arccos (a) + 36 0^{\circ} n

50 t + 2 0^{\circ} = arccos (\frac{1}{100}) + 36 0^{\circ} n, 50 t + 2 0^{\circ} = 36 0^{\circ} - arccos (\frac{1}{100}) + 36 0^{\circ} n

50 t + 2 0^{\circ} = arccos (\frac{1}{100}) + 36 0^{\circ} n, 50 t + 2 0^{\circ} = 36 0^{\circ} - arccos (\frac{1}{100}) + 36 0^{\circ} n

50 t + 2 0^{\circ} = arccos (\frac{1}{100}) + 36 0^{\circ} n

حلّ:

t = \frac{18 0 ^{\circ} n}{25} - 0. 4^{\circ} + \frac{arccos ( \frac{1}{100} )}{50}

50 t + 2 0^{\circ} = arccos (\frac{1}{100}) + 36 0^{\circ} n

انقل

2 0^{\circ}

إلى الجانب الأيمن

50 t + 2 0^{\circ} = arccos (\frac{1}{100}) + 36 0^{\circ} n

من الطرفين

2 0^{\circ}

اطرح

50 t + 2 0^{\circ} - 2 0^{\circ} = arccos (\frac{1}{100}) + 36 0^{\circ} n - 2 0^{\circ}

بسّط

50 t = arccos (\frac{1}{100}) + 36 0^{\circ} n - 2 0^{\circ}

50 t = arccos (\frac{1}{100}) + 36 0^{\circ} n - 2 0^{\circ}

50

اقسم الطرفين على

50 t = arccos (\frac{1}{100}) + 36 0^{\circ} n - 2 0^{\circ}

50

اقسم الطرفين على

\frac{50 t}{50} = \frac{arccos ( \frac{1}{100} )}{50} + \frac{36 0 ^{\circ} n}{50} - \frac{2 0 ^{\circ}}{50}

بسّط

\frac{50 t}{50} = \frac{arccos ( \frac{1}{100} )}{50} + \frac{36 0 ^{\circ} n}{50} - \frac{2 0 ^{\circ}}{50}

\frac{50 t}{50}

بسّط:

t

\frac{50 t}{50}

\frac{50}{50} = 1 :

اقسم الأعداد

= t

\frac{arccos ( \frac{1}{100} )}{50} + \frac{36 0 ^{\circ} n}{50} - \frac{2 0 ^{\circ}}{50}

بسّط:

\frac{18 0 ^{\circ} n}{25} - 0. 4^{\circ} + \frac{arccos ( \frac{1}{100} )}{50}

\frac{arccos ( \frac{1}{100} )}{50} + \frac{36 0 ^{\circ} n}{50} - \frac{2 0 ^{\circ}}{50}

جمّع التعابير المتشابهة

= \frac{36 0 ^{\circ} n}{50} - \frac{2 0 ^{\circ}}{50} + \frac{arccos ( \frac{1}{100} )}{50}

\frac{36 0 ^{\circ} n}{50} = \frac{18 0 ^{\circ} n}{25}

\frac{36 0 ^{\circ} n}{50}

2 :

إلغ العوامل المشتركة

= \frac{18 0 ^{\circ} n}{25}

\frac{2 0 ^{\circ}}{50} = 0. 4^{\circ}

\frac{2 0 ^{\circ}}{50}

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

: استخدم ميزات الكسور التالية

= \frac{18 0 ^{\circ}}{9 \cdot 50}

9 \cdot 50 = 450 :

اضرب الأعداد

= 0. 4^{\circ}

= \frac{18 0 ^{\circ} n}{25} - 0. 4^{\circ} + \frac{arccos ( \frac{1}{100} )}{50}

t = \frac{18 0 ^{\circ} n}{25} - 0. 4^{\circ} + \frac{arccos ( \frac{1}{100} )}{50}

t = \frac{18 0 ^{\circ} n}{25} - 0. 4^{\circ} + \frac{arccos ( \frac{1}{100} )}{50}

t = \frac{18 0 ^{\circ} n}{25} - 0. 4^{\circ} + \frac{arccos ( \frac{1}{100} )}{50}

50 t + 2 0^{\circ} = 36 0^{\circ} - arccos (\frac{1}{100}) + 36 0^{\circ} n

حلّ:

t = 7. 2^{\circ} - 0. 4^{\circ} + \frac{18 0 ^{\circ} n}{25} - \frac{arccos ( \frac{1}{100} )}{50}

50 t + 2 0^{\circ} = 36 0^{\circ} - arccos (\frac{1}{100}) + 36 0^{\circ} n

انقل

2 0^{\circ}

إلى الجانب الأيمن

50 t + 2 0^{\circ} = 36 0^{\circ} - arccos (\frac{1}{100}) + 36 0^{\circ} n

من الطرفين

2 0^{\circ}

اطرح

50 t + 2 0^{\circ} - 2 0^{\circ} = 36 0^{\circ} - arccos (\frac{1}{100}) + 36 0^{\circ} n - 2 0^{\circ}

بسّط

50 t = 36 0^{\circ} - arccos (\frac{1}{100}) + 36 0^{\circ} n - 2 0^{\circ}

50 t = 36 0^{\circ} - arccos (\frac{1}{100}) + 36 0^{\circ} n - 2 0^{\circ}

50

اقسم الطرفين على

50 t = 36 0^{\circ} - arccos (\frac{1}{100}) + 36 0^{\circ} n - 2 0^{\circ}

50

اقسم الطرفين على

\frac{50 t}{50} = 7. 2^{\circ} - \frac{arccos ( \frac{1}{100} )}{50} + \frac{36 0 ^{\circ} n}{50} - \frac{2 0 ^{\circ}}{50}

بسّط

\frac{50 t}{50} = 7. 2^{\circ} - \frac{arccos ( \frac{1}{100} )}{50} + \frac{36 0 ^{\circ} n}{50} - \frac{2 0 ^{\circ}}{50}

\frac{50 t}{50}

بسّط:

t

\frac{50 t}{50}

\frac{50}{50} = 1 :

اقسم الأعداد

= t

7. 2^{\circ} - \frac{arccos ( \frac{1}{100} )}{50} + \frac{36 0 ^{\circ} n}{50} - \frac{2 0 ^{\circ}}{50}

بسّط:

7. 2^{\circ} - 0. 4^{\circ} + \frac{18 0 ^{\circ} n}{25} - \frac{arccos ( \frac{1}{100} )}{50}

7. 2^{\circ} - \frac{arccos ( \frac{1}{100} )}{50} + \frac{36 0 ^{\circ} n}{50} - \frac{2 0 ^{\circ}}{50}

جمّع التعابير المتشابهة

= 7. 2^{\circ} + \frac{36 0 ^{\circ} n}{50} - \frac{2 0 ^{\circ}}{50} - \frac{arccos ( \frac{1}{100} )}{50}

7. 2^{\circ} = 7. 2^{\circ}

7. 2^{\circ}

2 :

إلغ العوامل المشتركة

= 7. 2^{\circ}

\frac{36 0 ^{\circ} n}{50} = \frac{18 0 ^{\circ} n}{25}

\frac{36 0 ^{\circ} n}{50}

2 :

إلغ العوامل المشتركة

= \frac{18 0 ^{\circ} n}{25}

\frac{2 0 ^{\circ}}{50} = 0. 4^{\circ}

\frac{2 0 ^{\circ}}{50}

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

: استخدم ميزات الكسور التالية

= \frac{18 0 ^{\circ}}{9 \cdot 50}

9 \cdot 50 = 450 :

اضرب الأعداد

= 0. 4^{\circ}

= 7. 2^{\circ} + \frac{18 0 ^{\circ} n}{25} - 0. 4^{\circ} - \frac{arccos ( \frac{1}{100} )}{50}

جمّع التعابير المتشابهة

= 7. 2^{\circ} - 0. 4^{\circ} + \frac{18 0 ^{\circ} n}{25} - \frac{arccos ( \frac{1}{100} )}{50}

t = 7. 2^{\circ} - 0. 4^{\circ} + \frac{18 0 ^{\circ} n}{25} - \frac{arccos ( \frac{1}{100} )}{50}

t = 7. 2^{\circ} - 0. 4^{\circ} + \frac{18 0 ^{\circ} n}{25} - \frac{arccos ( \frac{1}{100} )}{50}

t = 7. 2^{\circ} - 0. 4^{\circ} + \frac{18 0 ^{\circ} n}{25} - \frac{arccos ( \frac{1}{100} )}{50}

t = \frac{18 0 ^{\circ} n}{25} - 0. 4^{\circ} + \frac{arccos ( \frac{1}{100} )}{50}, t = 7. 2^{\circ} - 0. 4^{\circ} + \frac{18 0 ^{\circ} n}{25} - \frac{arccos ( \frac{1}{100} )}{50}

أظهر الحلّ بالتمثيل العشريّ

t = \frac{18 0 ^{\circ} n}{25} - 0. 4^{\circ} + \frac{1.56079 \dots}{50}, t = 7. 2^{\circ} - 0. 4^{\circ} + \frac{18 0 ^{\circ} n}{25} - \frac{1.56079 \dots}{50}

رسم

أمثلة شائعة

cos(2x)=sin(pi/2-x)

cos (2 x) = sin (\frac{π}{2} - x)

sin(x)=sin(50)

sin (x) = sin (5 0^{\circ})

solvefor n,y=-sin(2((3pi)/4+pin))2

so l v e f or n, y = - sin (2 (\frac{3 π}{4} + πn)) 2

tan(θ)= 18/7

tan (θ) = \frac{18}{7}

2cos^2(θ)=1+sin(θ)

2 cos^{2} (θ) = 1 + sin (θ)