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شائع علم المثلثات >

1/2 = 1/2*cos(4.2t+pi/6)

الحلّ

\frac{1}{2} = \frac{1}{2} \cdot cos (4.2 t + \frac{π}{6})

الحلّ

t = \frac{10 πn}{21} - \frac{5 π}{126}

درجات

t = - 7.14285 \dots^{\circ} + 85.71428 \dots^{\circ} n

خطوات الحلّ

\frac{1}{2} = \frac{1}{2} cos (4.2 t + \frac{π}{6})

بدّل الأطراف

\frac{1}{2} cos (4.2 t + \frac{π}{6}) = \frac{1}{2}

2

اضرب الطرفين بـ

\frac{1}{2} cos (4.2 t + \frac{π}{6}) = \frac{1}{2}

2

اضرب الطرفين بـ

2 \cdot \frac{1}{2} cos (4.2 t + \frac{π}{6}) = \frac{1 \cdot 2}{2}

بسّط

2 \cdot \frac{1}{2} cos (4.2 t + \frac{π}{6}) = \frac{1 \cdot 2}{2}

2 \cdot \frac{1}{2} cos (4.2 t + \frac{π}{6})

بسّط:

cos (4.2 t + \frac{π}{6})

2 \cdot \frac{1}{2} cos (4.2 t + \frac{π}{6})

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

:اضرب كسور

= \frac{1 \cdot 2}{2} cos (4.2 t + \frac{π}{6})

2 :

إلغ العوامل المشتركة

= cos (4.2 t + \frac{π}{6}) \cdot 1

cos (4.2 t + \frac{π}{6}) \cdot 1 = cos (4.2 t + \frac{π}{6}) :

اضرب

= cos (4.2 t + \frac{π}{6})

\frac{1 \cdot 2}{2}

بسّط:

1

\frac{1 \cdot 2}{2}

1 \cdot 2 = 2 :

اضرب الأعداد

= \frac{2}{2}

\frac{a}{a} = 1

فعّل القانون

= 1

cos (4.2 t + \frac{π}{6}) = 1

cos (4.2 t + \frac{π}{6}) = 1

cos (4.2 t + \frac{π}{6}) = 1

cos (4.2 t + \frac{π}{6}) = 1 :

حلول عامّة لـ

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

4.2 t + \frac{π}{6} = 0 + 2 πn

4.2 t + \frac{π}{6} = 0 + 2 πn

4.2 t + \frac{π}{6} = 0 + 2 πn

حلّ:

t = \frac{10 πn}{21} - \frac{5 π}{126}

4.2 t + \frac{π}{6} = 0 + 2 πn

0 + 2 πn = 2 πn

4.2 t + \frac{π}{6} = 2 πn

10

اضرب الطرفين بـ

4.2 t + \frac{π}{6} = 2 πn

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

4.2 t \cdot 10 + \frac{π}{6} \cdot 10 = 2 πn \cdot 10

بسّط

42 t + \frac{5 π}{3} = 20 πn

42 t + \frac{5 π}{3} = 20 πn

انقل

\frac{5 π}{3}

إلى الجانب الأيمن

42 t + \frac{5 π}{3} = 20 πn

من الطرفين

\frac{5 π}{3}

اطرح

42 t + \frac{5 π}{3} - \frac{5 π}{3} = 20 πn - \frac{5 π}{3}

بسّط

42 t = 20 πn - \frac{5 π}{3}

42 t = 20 πn - \frac{5 π}{3}

42

اقسم الطرفين على

42 t = 20 πn - \frac{5 π}{3}

42

اقسم الطرفين على

\frac{42 t}{42} = \frac{20 πn}{42} - \frac{\frac{5 π}{3}}{42}

بسّط

\frac{42 t}{42} = \frac{20 πn}{42} - \frac{\frac{5 π}{3}}{42}

\frac{42 t}{42}

بسّط:

t

\frac{42 t}{42}

\frac{42}{42} = 1 :

اقسم الأعداد

= t

\frac{20 πn}{42} - \frac{\frac{5 π}{3}}{42}

بسّط:

\frac{10 πn}{21} - \frac{5 π}{126}

\frac{20 πn}{42} - \frac{\frac{5 π}{3}}{42}

\frac{20 πn}{42} = \frac{10 πn}{21}

\frac{20 πn}{42}

2 :

إلغ العوامل المشتركة

= \frac{10 πn}{21}

\frac{\frac{5 π}{3}}{42} = \frac{5 π}{126}

\frac{\frac{5 π}{3}}{42}

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

: استخدم ميزات الكسور التالية

= \frac{5 π}{3 \cdot 42}

3 \cdot 42 = 126 :

اضرب الأعداد

= \frac{5 π}{126}

= \frac{10 πn}{21} - \frac{5 π}{126}

t = \frac{10 πn}{21} - \frac{5 π}{126}

t = \frac{10 πn}{21} - \frac{5 π}{126}

t = \frac{10 πn}{21} - \frac{5 π}{126}

t = \frac{10 πn}{21} - \frac{5 π}{126}

رسم

أمثلة شائعة

120=sqrt(83^2+75^2-2*83*75*cos(x))

120 = 8 3^{2} + 7 5^{2} - 2 \cdot 83 \cdot 75 \cdot cos (x)

cos(u)= 7/25

cos (u) = \frac{7}{25}

sin(x)+cos(x)=1,0<= x<2pi

sin (x) + cos (x) = 1, 0 \leq x < 2 π

solvefor x,cos^2(x+y)=sin^2(x+y)

so l v e f or x, cos^{2} (x + y) = sin^{2} (x + y)

cot^2(x)+3cot(x)+2=cot(x)+1

cot^{2} (x) + 3 cot (x) + 2 = cot (x) + 1