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kumpel [21]
3 years ago
15

Find the values of θ in the range 0≤θ≤360° which satisfy: 2 sin^2 θ - sinθ -1= 0

Mathematics
1 answer:
Sergio [31]3 years ago
7 0

Answer:

Step-by-step explanation:

Solving trig equations are just like solving "regular" equations. Let's get to it. First and foremost we are going to make a "u" substitution. You'll use that all the time in calculus, if you choose to go that route. Let

sin^2 \theta=u^2 and sinθ = u. Making the substitution, the equation becomes:

2u^2-u-1=0

That looks like something that can be factored, right? If you throw it into the quadratic formula you get the factors:

(u - 1)(2u + 1) = 0

By the Zero Product Property, either u - 1 = 0 or 2u + 1 = 0, so we will solve those, but not until after we back-substitute!

Putting sinθ back in for u:

sinθ - 1 = 0 so

sinθ = 1 and in the other equation:

2sinθ + 1 = 0 so

2sinθ = -1 and

sin\theta=-\frac{1}{2}

Get out the unit circle and look to where the sinθ has a value of 1. There's only one place in your interval, and it's at 90 degrees.

Now look to where the sinθ has a value of -1/2. There are 2 places within your interval, and those are at 210° and 330°. Now you're done!

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Hope that helps! :)
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3 years ago
What are the x-coordinates for the maximum points in the function f(x) = 4 cos(2x − π) from x = 0 to x = 2π? (1 point) a x = 3 p
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x-coordinates for the maximum points in any  function  f(x) by f'(x) =0 would be  x = π/2 and x= 3π/2.

<h3>How to obtain the maximum value of a function?</h3>

To find the maximum of a continuous and twice differentiable function f(x), we can firstly differentiate it with respect to x and equating it to 0 will give us critical points.

we want to find x-coordinates for the maximum points in any  function  f(x) by f'(x) =0

Given f(x)= 4cos(2x -π)

f'(x) = 0\\- 4sin(2x -\pi ) =0\\\\sin (2x -\pi ) =0 \\2x -\pi  = k\pi ...  k in Z

In general  x=(k+1)\pi /2

from x = 0 to x = 2π :

when k =0  then  x = π/2

when k =1  then x= π

when k =2  then x= 3π/2

when k =3  then x=2π

Thus, X-coordinates of maximum points are  x = π/2 and x= 3π/2

Learn more about maximum of a function here:

brainly.com/question/13333267

#SPJ4

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2 years ago
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