en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

solve for

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

Solution

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

+1

Degrees

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

Solution steps

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

Multiply both sides by

9.8

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

Multiply both sides by

9.8

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

Simplify

6400 sin (2 a) = 3430

6400 sin (2 a) = 3430

Divide both sides by

6400

6400 sin (2 a) = 3430

Divide both sides by

6400

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

Simplify

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

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

Apply trig inverse properties

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

General solutions for

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

Solve

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

2 a = arcsin (\frac{343}{640}) + 2 πn

Divide both sides by

2

2 a = arcsin (\frac{343}{640}) + 2 πn

Divide both sides by

2

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

Simplify

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

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

Solve

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

Divide both sides by

2

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

Divide both sides by

2

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

Simplify

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

Show solutions in decimal form

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

Popular Examples

tan(A)= 5/12 ,b=3

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

tan (2 β) = - \frac{4}{3}

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

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

3sec^2(x/2)-4sec(x/2)-4=0

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

tan(x)= 3/(10cos(x)),0<x<90

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