`12sin^2 (x) - 13sin(x) + 3 = 0` Use the Quadratic Formula to solve the equation in the interval `0,2pi)`. Then use a graphing utility to approximate the angle `x`.

Textbook Question

Chapter 5, 5.3 - Problem 59 - Precalculus (3rd Edition, Ron Larson).
See all solutions for this textbook.

1 Answer | Add Yours

gsarora17's profile pic

gsarora17 | (Level 2) Associate Educator

Posted on

`12sin^2(x)-13sin(x)+3=0`

using quadratic formula,

`sin(x)=(-(-13)+-sqrt((-13)^2-4*12*3))/(2*12)`

`sin(x)=(13+-sqrt(169-144))/24`

`sin(x)=(13+-sqrt(25))/24`

`sin(x)=(13+-5)/24=3/4,1/3`

Solutions of sin(x)=1/3 for the rangeĀ `0<=x<=2pi`

`x=arcsin(1/3) , x=pi-arcsin(1/3)`

Solutions of sin(x)=3/4 for the range are,

`x=arcsin(3/4) , x=pi-arcsin(3/4)`

Solutions areĀ `x=arcsin(1/3) , arcsin(3/4) , pi-arcsin(1/3) , pi-arcsin(3/4)`

See the attached graph,

x `~~` 0.3 , 0.8 , 2.3 , 2.8

Images:
This image has been Flagged as inappropriate Click to unflag
Image (1 of 1)

We’ve answered 318,911 questions. We can answer yours, too.

Ask a question