Explain how special right triangles, reference angles, and quadrants of a coordinate grid help us find the exact answer to the following: cos 210°.

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  cos(210°) = -(√3)/2

Step-by-step explanation:

The terminal ray of a 210° angle is in the third quadrant. The angle it makes with the -x axis is (210° -110°) = 30°. This is the "reference angle". In the 3rd quadrant, the x-coordinate of the terminal ray's intersection with the unit circle has a negative sign. This will be the sign of the cosine of the angle.

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The reference angle of 30° tells you that the trig functions of the angle can be found from the side ratios of the "special right triangle" with angles of 30°, 60°, and 90°. The side ratios, shortest to longest, in that triangle are 1 : √3 : 2.

The cosine of the angle is the ratio ...

  Cos = Adjacent/Hypotenuse

In the above special triangle, the side adjacent to the 30° angle is the one that is √3 ratio unis. The hypotenuse is 2 ratio units. So, the cosine of 30° is ...

  cos(30°) = (√3)/2

As we said above, the sign of the adjacent side of the reference angle for 210° has a negative value. (The hypotenuse is always considered to be positive.) Then the desired cosine is ...

  cos(210°) = -cos(30°)

  cos(210°) = -(√3)/2

the multiples of 15 are 15, 30,45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195,   210, 225, 240, 255, 270, 285, 300, 315, 330, 345, 360, 375,   390, 405, 420, 435, 450, 465, 480, 495, 510, 525, 540, 555, 570, 585, 600, 615, 630, 645, 660, 675, 690, 705, 720, and 735.

the factors of 15 are 1, 3, 5, and 15.

hope that , fam!

-une, your fren : )