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人気のある三角関数 >

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

解

解く

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

解

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

+1

度

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

解答ステップ

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

以下で両辺を乗じる:

9.8

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

以下で両辺を乗じる:

9.8

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

簡素化

6400 sin (2 a) = 3430

6400 sin (2 a) = 3430

以下で両辺を割る

6400

6400 sin (2 a) = 3430

以下で両辺を割る

6400

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

簡素化

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

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

三角関数の逆数プロパティを適用する

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

以下の一般解

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

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

解く

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

2 a = arcsin (\frac{343}{640}) + 2 πn

以下で両辺を割る

2

2 a = arcsin (\frac{343}{640}) + 2 πn

以下で両辺を割る

2

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

簡素化

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

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

解く

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

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

以下で両辺を割る

2

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

以下で両辺を割る

2

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

簡素化

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

10進法形式で解を証明する

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

グラフ

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