Byron S. answered • 11/01/14

Math and Science Tutor with an Engineering Background

The cosine function has positive values in the first and fourth quadrants, and negative values in the second and third. The value you found is in the second quadrant: π/2 < 1.97 < π

To find the corresponding angle in the third quadrant, you first need to find the reference angle.

π - φ = 1.97

φ = π - 1.97

This is the measure of the angle between the -x-axis and the angle you've found. To put this into the third quadrant, you need to add it to the -x-axis

π + φ = the 2nd answer.

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In general, when you have an angle and want to find similar angles in other quadrants, you'll use the following relationships between standard angle θ and reference angle φ. All 4 of these angles will have the same absolute value of each trig function. You'll need to learn which trig functions are positive and negative in which quadrants.

In QI: θ = φ

QII: θ = π - φ

QIII: θ = π + φ

QIV: θ = 2π - φ,

or θ = -φ for negative angles -π/2 < θ < 0