Question

"solve for the following trig ratios using the unit circle":

Answer 1

Answer:   -1

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Explanation:

The goal is to get that 1755 degree angle between 0 and 360, so we can refer to the unit circle later.

Subtract off 360 from this until we get to that target

• 1755 - 360 = 1395
• 1395 - 360 = 1035
• 1035 - 360 = 675
• 675 - 360 = 315

Or a shortcut could be

• 1755 - 4*360 = 315

The angles of 1755 degrees and 315 degrees are coterminal. They point in the same exact direction which is directly southeast in quadrant IV.

Now use the unit circle (see below) to find that

• sin(315) = -sqrt(2)/2
• cos(315) = sqrt(2)/2

Dividing those two items and simplifying gets us

tan(315) = sin(315)/cos(315) = -1

Then we go from tan(315) = -1 to tan(1755)  = -1