Select all the correct answers.If the measure of angle 𝜃 is 3⁢𝜋4 , which statements are true? The measure of the reference angle is 30∘ . cos⁡(𝜃)=22 tan⁡(𝜃)=1 sin⁡(𝜃)=22 The measure of the reference angle is 60∘ . The measure of the reference angle is 45∘ .

The measure of angle 𝜃 is given as 3𝜋/4. This is in radians and it corresponds to 135 degrees in the unit circle.

1. The measure of the reference angle is 30∘: This statement is false. The reference angle is the acute angle that the terminal side of the given angle makes with the x-axis. For an angle of 135 degrees, the reference angle is 45 degrees, not 30 degrees.

2. cos⁡(𝜃)=22: This statement is false. The cosine of 135 degrees or 3𝜋/4 radians is -1/√2 or -√2/2, not 22.

3. tan⁡(𝜃)=1: This statement is false. The tangent of 135 degrees or 3𝜋/4 radians is -1, not 1.

4. sin⁡(𝜃)=22: This statement is false. The sine of 135 degrees or 3𝜋/4 radians is 1/√2 or √2/2, not 22.

5. The measure of the reference angle is 60∘: This statement is false. As mentioned earlier, the reference angle for 135 degrees is 45 degrees, not 60 degrees.

6. The measure of the reference angle is 45∘: This statement is true. The reference angle for 135 degrees or 3𝜋/4 radians is indeed 45 degrees.