Question

The angle measures associated with which set of ordered pairs share the same reference angle

Answer 1

Answer:

Option 3 is right.

Step-by-step explanation:

Reference angle of x is obtained by either 180-x, 180+x. or 360-x depending on the posiiton of terminal whether II quadrant or iv quadrant, or iii quadrant, etc.

In whatever way we find reference angles,

cos will remain cos only and sin will remain sin only there may be only changes in sign.

Of all the ordered pairs given, we find that I, II, and Iv there is a switch over form cos to sine and sin to cos.  Hence these options cannot be for reference angles.

III option is $(-\frac{1}{2} ,\frac{-\sqrt{3} }{2} )(\frac{1}{2} ,\frac{\sqrt{3} }{2} )$

show that both sign and cos changed sign.  This is possible only in III quadrant.

ie reference angle of orignal angle t = 180+t

SO this option is right.

Answer 2

set of ordered pairs share the same reference angle is choice no. 3

Further explanation

Angles can be formed from two ray lines that have the same starting point

Commonly used terms include vertex,corner point, and angle size

The magnitude of the angle is usually expressed in degrees

Naming angles can be with one letter according to the vertex or with three letters with the vertex placed between two other letters

In trigonometry an angle can be described from two sides namely the terminal side and the origin / initial side (along the positive x axis)

The terminal side is the side that can be located anywhere and shows the size of an angle.

Reference angle  is the smallest angle between the terminal side and the x-axis.

The reference angle is always positive wherever the quadrant is

The reference angle is always less than or equal to 90 °

The formula reference angle (θ) for each quadrant

• Quadrant I

Same as θ

• Quadrant II

180 - θ

• Quadrant III

θ - 180

• Quadrant IV

360 - θ

From the set of ordered pairs from the angle above, it can be seen that the angle value is the value of the special angle of the sin and cos functions, which are

$\dfrac{1}{2}~and~\dfrac{1}{2}\sqrt{3}$

Sin function is positive in quadrants 1 and 2

Cos function is positive in quadrants 1 and 4

From the available answer choices, the reference angle will be the same value if the existing pair of angles are in the same ordered location and have the same value but only have different marks due to differences in quadrant location

From this condition only option 3 fulfills a reference angle of 30, which is in quadrants 3 and 1

$-\dfrac{1}{2} ,-\dfrac{1}{2}\sqrt{3} \Rightarrow -sin~30,-cos~30\Rightarrow Quadrant~3$

$\dfrac{1}{2} ,\dfrac{1}{2}\sqrt{3} \Rightarrow sin~30,cos~30\Rightarrow Quadrant~1$

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Keywords: angle, reference angle, quadrant, sin, cos