22aegirdham
contestada

if the measure of angle 0 is 11pi/6 which statements are true?

the measure of the reference angle is 45°

the measure of the reference angle is 60°

cos(0)= square root 3 /2

sin(0)= 1/2

tan(0)=1

the measure of the reference angle is 30°
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Respuesta :

Answer: cos of theta= square root 3//2 and the measure of the reference angle is 30

Step-by-step explanation:

11π/6 reference angle is π/6 which is 30 degree so the measure of the reference angle is 30 degrees is correct. sin of 330 is sqr root of 3 divided by 2. Since it in the 4th quadrant and cos refers to x -axis it is positive.

MrRoyal

The following options are correct:

The measure of the reference angle is: [tex]30 ^o[/tex]

[tex]\cos(\theta) = \frac{\sqrt 3}{2}[/tex]

The reference angle of an angle is the smallest acute angle between the terminal arm of a quadrant and the x-axis.

Given that:

[tex]\theta = \frac{11\pi}{6}[/tex]

First, we convert to degrees

[tex]\theta = \frac{11\pi}{6} * 180\pi[/tex]

[tex]\theta = \frac{11}{6} * 180[/tex]

[tex]\theta = 11 * 30[/tex]

[tex]\theta = 330^o[/tex]

Since 330 is closer to 360, the reference angle ([tex]\alpha[/tex]) is:

[tex]\theta = 360 - \alpha[/tex]

Substitute [tex]\theta = 330^o[/tex]

[tex]330 = 360 - \alpha[/tex]

Collect like terms

[tex]\alpha= 360 - 330[/tex]

[tex]\alpha= 30[/tex]

Hence, the measure of the reference angle is: [tex]30 ^o[/tex]

[tex]\alpha= 30[/tex] means that the reference angle is in the first quadrant

[tex]\theta = 330^o[/tex] means that this angle is in the fourth quadrant

In the first and the fourth quadrants,

[tex]\cos(\theta) = \cos(\alpha)[/tex]

Substitute [tex]\alpha= 30[/tex]

[tex]\cos(\theta) = \cos(30)[/tex]

In trigonometry:

[tex]\cos(30) = \frac{\sqrt 3}{2}[/tex]

So:

[tex]\cos(\theta) = \frac{\sqrt 3}{2}[/tex]

Read more about reference angles at:

https://brainly.com/question/1603873

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