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شائع علم المثلثات >

arcsin(3/5)+arccos(x)=pi

الحلّ

arcsin (\frac{3}{5}) + arccos (x) = π

الحلّ

x = - \frac{4}{5}

خطوات الحلّ

arcsin (\frac{3}{5}) + arccos (x) = π

انقل

arcsin (\frac{3}{5})

إلى الجانب الأيمن

arcsin (\frac{3}{5}) + arccos (x) = π

من الطرفين

arcsin (\frac{3}{5})

اطرح

arcsin (\frac{3}{5}) + arccos (x) - arcsin (\frac{3}{5}) = π - arcsin (\frac{3}{5})

بسّط

arccos (x) = π - arcsin (\frac{3}{5})

arccos (x) = π - arcsin (\frac{3}{5})

Apply trig inverse properties

arccos (x) = π - arcsin (\frac{3}{5})

arccos (x) = a \Rightarrow x = cos (a)

x = cos (π - arcsin (\frac{3}{5}))

cos (π - arcsin (\frac{3}{5})) = - \frac{4}{5}

cos (π - arcsin (\frac{3}{5}))

Rewrite using trig identities:

cos (π) cos (arcsin (\frac{3}{5})) + sin (π) sin (arcsin (\frac{3}{5}))

cos (π - arcsin (\frac{3}{5}))

cos (s - t) = cos (s) cos (t) + sin (s) sin (t)

:فعّل متطابقة الطرح لزوايا

= cos (π) cos (arcsin (\frac{3}{5})) + sin (π) sin (arcsin (\frac{3}{5}))

= cos (π) cos (arcsin (\frac{3}{5})) + sin (π) sin (arcsin (\frac{3}{5}))

استخدم المتطابقة الأساسيّة التالية:

cos (π) = (- 1)

cos (π)

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}

= (- 1)

Rewrite using trig identities:

cos (arcsin (\frac{3}{5})) = \frac{4}{5}

cos (arcsin (\frac{3}{5}))

Rewrite using trig identities:

cos (arcsin (\frac{3}{5})) = 1 - (\frac{3}{5})^{2}

cos (arcsin (x)) = 1 - x^{2} :

استخدم المتطابقة التالية

= 1 - (\frac{3}{5})^{2}

= 1 - (\frac{3}{5})^{2}

بسّط

= \frac{4}{5}

استخدم المتطابقة الأساسيّة التالية:

sin (π) = 0

sin (π)

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 0

Rewrite using trig identities:

sin (arcsin (\frac{3}{5})) = \frac{3}{5}

sin (arcsin (x)) = x :

استخدم المتطابقة التالية

= \frac{3}{5}

= (- 1) \frac{4}{5} + 0 \cdot \frac{3}{5}

بسّط

= - \frac{4}{5}

x = - \frac{4}{5}

x = - \frac{4}{5}

رسم

أمثلة شائعة

cos (θ) = \frac{6}{7}

2cos(2θ)+7sin(θ)=5

2 cos (2 θ) + 7 sin (θ) = 5

cos (x) = \frac{5}{10}

sin((8pi)/(23))=sin(x)

sin (\frac{8 π}{23}) = sin (x)

-2sin(x)-4cos(2x)=0

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