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

Solución

resolver para

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

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

Grados

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

Pasos de solución

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

Multiplicar ambos lados por

9.8

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

Multiplicar ambos lados por

9.8

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

Simplificar

6400 sin (2 a) = 3430

6400 sin (2 a) = 3430

Dividir ambos lados entre

6400

6400 sin (2 a) = 3430

Dividir ambos lados entre

6400

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

Simplificar

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

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

Aplicar propiedades trigonométricas inversas

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

Soluciones generales para

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

Resolver

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

2 a = arcsin (\frac{343}{640}) + 2 πn

Dividir ambos lados entre

2

2 a = arcsin (\frac{343}{640}) + 2 πn

Dividir ambos lados entre

2

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

Simplificar

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

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

Resolver

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

Dividir ambos lados entre

2

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

Dividir ambos lados entre

2

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

Simplificar

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

Mostrar soluciones en forma decimal

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

tan (A) = \frac{5}{12}, b = 3

tan (2 β) = - \frac{4}{3}

4 cos^{2} (x) - 5 cos (x) - 6 = 0

3 sec^{2} (\frac{x}{2}) - 4 sec (\frac{x}{2}) - 4 = 0

tan (x) = \frac{3}{10 cos ( x )}, 0^{\circ} < x < 9 0^{\circ}