Wednesday

December 17, 2014

December 17, 2014

Posted by **greeny** on Wednesday, October 3, 2012 at 12:25am.

2 sin 4x = 1

i got 5 pi/24 and pi/ 24 but my teacher said that there should be eight solutions. what would those be and how would i find it"

- PRECALC -
**Bosnian**, Wednesday, October 3, 2012 at 7:35am2 sin 4 x = 1 Divide both sides by 2

sin 4 x = 1 / 2

Take the inverse sine of both sides :

4 x = sin ^ - 1 ( 1 / 2 )

________________________________________

Remark :

sin ^ - 1 ( 1 / 2 ) =

pi / 6 + 2 pi n

OR

5 pi / 6 + 2 pi n

Where n is an integer

________________________________________

4 x = pi / 6 + 2 pi n

OR

4 x = 5 pi / 6 + 2 pi n

Divide both sides by 4

x = pi / 24 + pi n / 2

OR

x = 5 pi / 24 + pi n / 2

For n = 0

x = pi / 24 + pi * 0 / 2

x = pi / 24

OR

x = 5 pi / 24 + pi * 0 / 2

x = 5 pi / 24

For n = 1

x = pi / 24 + pi * 1 / 2

x = pi / 24 + pi / 2

x = pi / 24 + 12 pi / 24

x = 13 pi / 24

OR

x = 5 pi / 24 + pi * 1 / 2

x = 5 pi / 24 + pi / 2

x = 5 pi / 24 + 12 pi / 24

x = 17 pi / 24

For n = 2

x = pi / 24 + pi * 2 / 2

x = pi / 24 + pi

x = pi / 24 + 24 pi / 24

x = 25 pi / 24

OR

x = 5 pi / 24 + pi * 2 / 2

x = 5 pi / 24 + pi

x = 5 pi / 24 + 24 pi / 24

x = 29 pi / 24

For n = 3

x = pi / 24 + pi * 3 / 2

x = pi / 24 + 3 pi / 2

x = pi / 24 + 3 * 12 pi / 24

x = pi / 24 + 36 pi / 24

x = 37 pi / 24

OR

x = 5 pi / 24 + pi * 3 / 2

x = 5 pi / 24 + 3 pi / 2

x = 5 pi / 24 + 3 * 12 pi / 24

x = 5 pi / 24 + 36 pi / 24

x = 41 pi / 24

Solutions :

x1 = pi / 24

x2 = 5 pi / 24

x3 = 13 pi / 24

x4 = 17 pi / 24

x5 = 25 pi / 24

x6 = 29 pi / 24

x7 = 37 pi / 24

x8 = 41 pi / 24

**Answer this Question**

**Related Questions**

Math - Find the exact value of the trigonometric function given that sin u = 5/...

Math - Find the exact value of the trigonometric function given that sin u = 5/...

Precalc. - solve the equation on the interval [0,2pi) sin^2x=1

Solve Inequality - Solve the inequality. Express your solution using interval ...

Precalc - Hello, good afternoon. I need help with my precalc hw. we are learning...

Trigonometry - I need help with I just can't seem to get anywhere. this is as ...

Math(about to fail because of this question) - Can someone please help me with ...

calculus - find max, min and saddle points of the give function f(x,y)=sin(x)+...

Physics Word Problem - 4. An automobile is traveling at 30 km/hr. It accelerates...

algebra - I have a few problems I need you to take a look at and tell me if I ...