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شائع علم المثلثات >

tan(3x+25)*160-1=0

الحلّ

tan (3 x + 2 5^{\circ}) \cdot 16 0^{\circ} - 1 = 0

الحلّ

x = \frac{18 0 ^{\circ} n}{3} - 8.33333 \dots^{\circ} + \frac{0.34387 \dots}{3}

+1

راديان

x = - \frac{5 π}{108} + \frac{0.34387 \dots}{3} + \frac{π}{3} n

خطوات الحلّ

tan (3 x + 2 5^{\circ}) \cdot 16 0^{\circ} - 1 = 0

انقل

1

إلى الجانب الأيمن

tan (3 x + 2 5^{\circ}) 16 0^{\circ} - 1 = 0

للطرفين

1

أضف

tan (3 x + 2 5^{\circ}) 16 0^{\circ} - 1 + 1 = 0 + 1

بسّط

tan (3 x + 2 5^{\circ}) 16 0^{\circ} = 1

tan (3 x + 2 5^{\circ}) 16 0^{\circ} = 1

9

اضرب الطرفين بـ

tan (3 x + 2 5^{\circ}) 16 0^{\circ} = 1

9

اضرب الطرفين بـ

9 tan (3 x + 2 5^{\circ}) 16 0^{\circ} = 1 \cdot 9

بسّط

144 0^{\circ} tan (3 x + 2 5^{\circ}) = 9

144 0^{\circ} tan (3 x + 2 5^{\circ}) = 9

144 0^{\circ}

اقسم الطرفين على

144 0^{\circ} tan (3 x + 2 5^{\circ}) = 9

144 0^{\circ}

اقسم الطرفين على

\frac{144 0 ^{\circ} tan ( 3 x + 2 5 ^{\circ} )}{144 0 ^{\circ}} = \frac{9}{144 0 ^{\circ}}

بسّط

tan (3 x + 2 5^{\circ}) = \frac{9}{144 0 ^{\circ}}

tan (3 x + 2 5^{\circ}) = \frac{9}{144 0 ^{\circ}}

Apply trig inverse properties

tan (3 x + 2 5^{\circ}) = \frac{9}{144 0 ^{\circ}}

tan (3 x + 2 5^{\circ}) = \frac{9}{144 0 ^{\circ}} :

حلول عامّة لـ

tan (x) = a \Rightarrow x = arctan (a) + 18 0^{\circ} n

3 x + 2 5^{\circ} = arctan (\frac{9}{144 0 ^{\circ}}) + 18 0^{\circ} n

3 x + 2 5^{\circ} = arctan (\frac{9}{144 0 ^{\circ}}) + 18 0^{\circ} n

3 x + 2 5^{\circ} = arctan (\frac{9}{144 0 ^{\circ}}) + 18 0^{\circ} n

حلّ:

x = \frac{18 0 ^{\circ} n}{3} - 8.33333 \dots^{\circ} + \frac{arctan ( \frac{9}{144 0 ^{\circ}} )}{3}

3 x + 2 5^{\circ} = arctan (\frac{9}{144 0 ^{\circ}}) + 18 0^{\circ} n

انقل

2 5^{\circ}

إلى الجانب الأيمن

3 x + 2 5^{\circ} = arctan (\frac{9}{144 0 ^{\circ}}) + 18 0^{\circ} n

من الطرفين

2 5^{\circ}

اطرح

3 x + 2 5^{\circ} - 2 5^{\circ} = arctan (\frac{9}{144 0 ^{\circ}}) + 18 0^{\circ} n - 2 5^{\circ}

بسّط

3 x = arctan (\frac{9}{144 0 ^{\circ}}) + 18 0^{\circ} n - 2 5^{\circ}

3 x = arctan (\frac{9}{144 0 ^{\circ}}) + 18 0^{\circ} n - 2 5^{\circ}

3

اقسم الطرفين على

3 x = arctan (\frac{9}{144 0 ^{\circ}}) + 18 0^{\circ} n - 2 5^{\circ}

3

اقسم الطرفين على

\frac{3 x}{3} = \frac{arctan ( \frac{9}{144 0 ^{\circ}} )}{3} + \frac{18 0 ^{\circ} n}{3} - \frac{2 5 ^{\circ}}{3}

بسّط

\frac{3 x}{3} = \frac{arctan ( \frac{9}{144 0 ^{\circ}} )}{3} + \frac{18 0 ^{\circ} n}{3} - \frac{2 5 ^{\circ}}{3}

\frac{3 x}{3}

بسّط:

x

\frac{3 x}{3}

\frac{3}{3} = 1 :

اقسم الأعداد

= x

\frac{arctan ( \frac{9}{144 0 ^{\circ}} )}{3} + \frac{18 0 ^{\circ} n}{3} - \frac{2 5 ^{\circ}}{3}

بسّط:

\frac{18 0 ^{\circ} n}{3} - 8.33333 \dots^{\circ} + \frac{arctan ( \frac{9}{144 0 ^{\circ}} )}{3}

\frac{arctan ( \frac{9}{144 0 ^{\circ}} )}{3} + \frac{18 0 ^{\circ} n}{3} - \frac{2 5 ^{\circ}}{3}

جمّع التعابير المتشابهة

= \frac{18 0 ^{\circ} n}{3} - \frac{2 5 ^{\circ}}{3} + \frac{arctan ( \frac{9}{144 0 ^{\circ}} )}{3}

\frac{2 5 ^{\circ}}{3} = 8.33333 \dots^{\circ}

\frac{2 5 ^{\circ}}{3}

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

: استخدم ميزات الكسور التالية

= \frac{90 0 ^{\circ}}{36 \cdot 3}

36 \cdot 3 = 108 :

اضرب الأعداد

= 8.33333 \dots^{\circ}

= \frac{18 0 ^{\circ} n}{3} - 8.33333 \dots^{\circ} + \frac{arctan ( \frac{9}{144 0 ^{\circ}} )}{3}

x = \frac{18 0 ^{\circ} n}{3} - 8.33333 \dots^{\circ} + \frac{arctan ( \frac{9}{144 0 ^{\circ}} )}{3}

x = \frac{18 0 ^{\circ} n}{3} - 8.33333 \dots^{\circ} + \frac{arctan ( \frac{9}{144 0 ^{\circ}} )}{3}

x = \frac{18 0 ^{\circ} n}{3} - 8.33333 \dots^{\circ} + \frac{arctan ( \frac{9}{144 0 ^{\circ}} )}{3}

x = \frac{18 0 ^{\circ} n}{3} - 8.33333 \dots^{\circ} + \frac{arctan ( \frac{9}{144 0 ^{\circ}} )}{3}

أظهر الحلّ بالتمثيل العشريّ

x = \frac{18 0 ^{\circ} n}{3} - 8.33333 \dots^{\circ} + \frac{0.34387 \dots}{3}

رسم

أمثلة شائعة

5 cos (x) = 1

3cos(x)+5=7,0<= x<= 2pi

3 cos (x) + 5 = 7, 0 \leq x \leq 2 π

9sin(x/2)+9cos(x)=0

9 sin (\frac{x}{2}) + 9 cos (x) = 0

sin^2(x)-sin(x)=2,0<= x<= 2pi

sin^{2} (x) - sin (x) = 2, 0 \leq x \leq 2 π

cos (θ) = \frac{33}{55}