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شائع علم المثلثات >

(sin(x))/(tan(x))=-0.375

الحلّ

\frac{sin ( x )}{tan ( x )} = - 0.375

الحلّ

x = 1.95519 \dots + 2 πn, x = - 1.95519 \dots + 2 πn

+1

درجات

x = 112.02431 \dots^{\circ} + 36 0^{\circ} n, x = - 112.02431 \dots^{\circ} + 36 0^{\circ} n

خطوات الحلّ

\frac{sin ( x )}{tan ( x )} = - 0.375

من الطرفين

- 0.375

اطرح

\frac{sin ( x )}{tan ( x )} + 0.375 = 0

Rewrite using trig identities

0.375 + \frac{sin ( x )}{tan ( x )}

tan (x) = \frac{sin ( x )}{cos ( x )}

:Use the basic trigonometric identity

= 0.375 + \frac{sin ( x )}{\frac{s i n ( x )}{c o s ( x )}}

\frac{sin ( x )}{\frac{s i n ( x )}{c o s ( x )}} = cos (x)

\frac{sin ( x )}{\frac{s i n ( x )}{c o s ( x )}}

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

: استخدم ميزات الكسور التالية

= \frac{sin ( x ) cos ( x )}{sin ( x )}

sin (x) :

إلغ العوامل المشتركة

= cos (x)

= 0.375 + cos (x)

0.375 + cos (x) = 0

انقل

0.375

إلى الجانب الأيمن

0.375 + cos (x) = 0

من الطرفين

0.375

اطرح

0.375 + cos (x) - 0.375 = 0 - 0.375

بسّط

cos (x) = - 0.375

cos (x) = - 0.375

Apply trig inverse properties

cos (x) = - 0.375

cos (x) = - 0.375 :

حلول عامّة لـ

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

x = arccos (- 0.375) + 2 πn, x = - arccos (- 0.375) + 2 πn

x = arccos (- 0.375) + 2 πn, x = - arccos (- 0.375) + 2 πn

أظهر الحلّ بالتمثيل العشريّ

x = 1.95519 \dots + 2 πn, x = - 1.95519 \dots + 2 πn

رسم

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