Solve the equation 2 plus 2 sine theta equals 4 cosine...

Solve the equation. 2 plus 2 sine theta equals 4 cosine squared theta2+2sinθ=4cos2θ Question content area bottom Part 1 What is the solution in the interval 0 less than or equals theta less than 2 pi0≤θ<2π? Select the correct choice and fill in any answer boxes in your choice below.

Transcript

00:01 Problem for being asked to solve the given equation for values of theta between 0 and 2 pi.

00:06 So notice that your answers need to be in radiant mode.

00:09 So the first thing i notice, we have two different trig functions.

00:12 We have cosine and we have sine.

00:14 So the first thing we're going to want to try and do is rewrite this equation so that way they both have the same trig function.

00:21 Well, in order to do this, i'm going to use the pythagrin identity that says the sine square the theta plus the cosine square the theta is equal to 1.

00:30 Because i can solve for the cosine square the theta by subtracting the sine square the theta from both sides.

00:37 So that will leave us with the cosine square the theta equal to 1 minus sine square the theta.

00:47 So now, in place of cosine squared theta in our problem, i'm going to substitute in 1 minus sine square the theta.

00:53 So we're going to have 2 times 1 minus sine square the theta, and this is equal to 2 plus the sine of theta.

01:01 So again, now we only have the sine function.

01:04 Next thing i'm going to do is get rid of the parentheses by distributing, well, 2 times 1 is 2, and 2 times negative sine square the theta, and the right -hand side stays the same.

01:18 So now the next thing i'm going to do is set my equation equal to 0.

01:21 So i'm going to move the terms on the left over to the right.

01:24 So first, i'm going to subtract 2, but when i do that, both of my 2 is cancel.

01:29 At the same time, i can add 2 sine square the theta to both sides of the equation, because the terms on the left cancel.

01:38 So i'll have zero equals, and if i put this in standard form, i'm going to have two sine square the theta plus the sine of theta.

01:47 Next, what i'm going to do is i'm going to solve this by factoring.

01:51 I'm going to take out a gcf of sine of theta...

Question

Solve the equation. 2 plus 2 sine theta equals 4 cosine squared theta2+2sinθ=4cos2θ Question content area bottom Part 1 What is the solution in the interval 0 less than or equals theta less than 2 pi0≤θ<2π? Select the correct choice and fill in any answer boxes in your choice below.

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