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شائع علم المثلثات >

solvefor a,(80^2sin(2a))/(9.8)=350

الحلّ

solve for

a, \frac{8 0 ^{2} sin ( 2 a )}{9.8} = 350

الحلّ

a = \frac{0.56561 \dots}{2} + πn, a = \frac{π}{2} - \frac{0.56561 \dots}{2} + πn

+1

درجات

a = 16.20375 \dots^{\circ} + 18 0^{\circ} n, a = 73.79624 \dots^{\circ} + 18 0^{\circ} n

خطوات الحلّ

\frac{8 0 ^{2} sin ( 2 a )}{9.8} = 350

9.8

اضرب الطرفين بـ

\frac{8 0 ^{2} sin ( 2 a )}{9.8} = 350

9.8

اضرب الطرفين بـ

\frac{9.8 \cdot 8 0 ^{2} sin ( 2 a )}{9.8} = 350 \cdot 9.8

بسّط

6400 sin (2 a) = 3430

6400 sin (2 a) = 3430

6400

اقسم الطرفين على

6400 sin (2 a) = 3430

6400

اقسم الطرفين على

\frac{6400 sin ( 2 a )}{6400} = \frac{3430}{6400}

بسّط

sin (2 a) = \frac{343}{640}

sin (2 a) = \frac{343}{640}

Apply trig inverse properties

sin (2 a) = \frac{343}{640}

sin (2 a) = \frac{343}{640} :

حلول عامّة لـ

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

2 a = arcsin (\frac{343}{640}) + 2 πn, 2 a = π - arcsin (\frac{343}{640}) + 2 πn

2 a = arcsin (\frac{343}{640}) + 2 πn, 2 a = π - arcsin (\frac{343}{640}) + 2 πn

2 a = arcsin (\frac{343}{640}) + 2 πn

حلّ:

a = \frac{arcsin ( \frac{343}{640} )}{2} + πn

2 a = arcsin (\frac{343}{640}) + 2 πn

2

اقسم الطرفين على

2 a = arcsin (\frac{343}{640}) + 2 πn

2

اقسم الطرفين على

\frac{2 a}{2} = \frac{arcsin ( \frac{343}{640} )}{2} + \frac{2 πn}{2}

بسّط

a = \frac{arcsin ( \frac{343}{640} )}{2} + πn

a = \frac{arcsin ( \frac{343}{640} )}{2} + πn

2 a = π - arcsin (\frac{343}{640}) + 2 πn

حلّ:

a = \frac{π}{2} - \frac{arcsin ( \frac{343}{640} )}{2} + πn

2 a = π - arcsin (\frac{343}{640}) + 2 πn

2

اقسم الطرفين على

2 a = π - arcsin (\frac{343}{640}) + 2 πn

2

اقسم الطرفين على

\frac{2 a}{2} = \frac{π}{2} - \frac{arcsin ( \frac{343}{640} )}{2} + \frac{2 πn}{2}

بسّط

a = \frac{π}{2} - \frac{arcsin ( \frac{343}{640} )}{2} + πn

a = \frac{π}{2} - \frac{arcsin ( \frac{343}{640} )}{2} + πn

a = \frac{arcsin ( \frac{343}{640} )}{2} + πn, a = \frac{π}{2} - \frac{arcsin ( \frac{343}{640} )}{2} + πn

أظهر الحلّ بالتمثيل العشريّ

a = \frac{0.56561 \dots}{2} + πn, a = \frac{π}{2} - \frac{0.56561 \dots}{2} + πn

رسم

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