Find two values of θ, 0 ≤ θ

Question

Find two values of θ, 0 ≤ θ < 2𝜋, that satisfy each equation.

sin θ = √2/2

Accepted Answer

Hello, everyone. We are asked to determine two possible solutions for theta where theta is between zero and two pi but could be zero. And they fulfill the equation. We are provided we are given the tangent of theta equals radical three divided by three. Our answer choices are a, theta equals pi divided by six and theta equals pi divided by two B. Theta equals pi divided by six and theta equals five pi divided by six C. Theta equals pi divided by six and theta equals seven pi divided by six D. Theta equals pi divided by six and theta equals three pi divided by two. All right. First thing we know we know that the tangent of theta will equal radical three divided by three. So this is positive. So we don't have to worry about which quadrant we're starting out in, we'll start in the first quadrant. And so if we think about the arc tangent of radical three divided by three, we will find that the angle that will match for the is pi divided by six. So knowing that we know this is gonna be one of our possible solutions since we want two possible solutions, we need to find another angle that has the same measure. Um So since the period of tangent is pi, we are gonna add pie to pie divided by six. So our second answer or possible solution would be pi divided by six plus pi. It would be the same as saying pi divided by six plus six, pi divided by six. And this comes out to seven pi divided by six. So that is gonna be another possible solution. And now that we have two, we can match them to our answer choices and answer choice. C theta equals pi divided by six and theta equals seven pi divided by six. Have a nice day.

Find two values of θ, 0 ≤ θ < 2𝜋, that satisfy each equation.
sin θ = √2/2

Key Concepts

Unit Circle and Angle Measurement

Sine Function Values and Their Range

Finding Multiple Solutions in One Period

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