What is the right choice for question 5) ? http://postimg.org/image/3y8s18xxn/

What is the right choice for question 5) ?

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Expert Answers
mvcdc eNotes educator| Certified Educator

The equation is:

`3cos^2 x + cos x - 1 = 0`

Notice that this equation resembles a quadratic equation. Hence, it will be easier for us to solve this if we transform it first to a quadratic equation, which we can solve by using the quadratic formula.

We first make the assignment `u = cos x` .

Hence, the equation becomes:

`3u^2 + u - 1 = 0` to which we apply the quadratic formula:

`u = (-1 pm sqrt(1^2 - 4*3*-1))/(2*3)`

This gives us:

`u = (-1 pm sqrt(13))/6`

or `u approx 0.434 ; u approx -0.768`

Now, we transform this back to cosine. We know that `u = cos x` .

This means that:

`cos x = 0.434` or `cos x = -0.768`

Applying `arccos` on both sides:

`x = cos^-1(0.434) = 1.12`

`x = cos^-1(-0.768) = 2.45`

Hence, the correct answer is b 1.12 and 2.45.