document.write( "Question 1156790: How do you figure out which quadrant the terminal side of each angle lies in based on if sin/cos/tan, etc. is greater than or less than theta?\r
\n" ); document.write( "\n" ); document.write( "For example, Sec(theta)=13/12, sin(theta)<0 \n" ); document.write( "

Algebra.Com's Answer #779551 by Theo(13342) $\"\"$ $\"About$

You can put this solution on YOUR website!
the quadrant that the angle is in is based on the sign of the trig function.
\n" ); document.write( "in the first quadrant, all trig functions are positive.
\n" ); document.write( "you concentrate on sine, cosine, and tangent.
\n" ); document.write( "since cosecant is 1/sine and secant is 1/cosine and cotangent is 1/tangent, they will follow the sign of their reciprocals of sine, cosine, and tangent.
\n" ); document.write( "the hypotenuse of the triangle formed by the angle is always positive because it is the square root of (x^2 + y^2) which is always positive because x^2 and y^2 are always positive, regardless of the underlying sign of x and y.
\n" ); document.write( "the rules are as follows:
\n" ); document.write( "sine, cosine, and tangent are all positive in the first quadrant.
\n" ); document.write( "in the second quadrant, sine is positive and cosine is negative and tangent is negative because it is equal to sine / cosine which is a positive divided by a negative, therefore negative.
\n" ); document.write( "in the third quadrant, sine is negative and cosine is negative and tangent is positive because tangent is sine / cosine which is a negative divided by a negative which is positive.
\n" ); document.write( "in the fourth quadrant, sine is negative and cosine is positive and tangent is negative because it is equal to sine / cosine which is a negative divided by a positive which is negative.
\n" ); document.write( "here's a reference on the unit circle that you might find informative.
\n" ); document.write( "https://www.purplemath.com/modules/unitcirc.htm
\n" ); document.write( "if you have any further questions regarding how to determine the quadrant that the angle is in, feel free to email me at dtheophilis@gmail.com.
\n" ); document.write( "keep in mind that, in the first quadrant, all trig functions are positive and sine and cosine are always between 0 and 1, while tangent can be any value depending on the ratio of sine / cosine.
\n" ); document.write( "the quadrant that the angle is in is determined by the sign of the trig function that the angle is derived from.
\n" ); document.write( "the rules for what quadrant the angle is in are as follows.
\n" ); document.write( "if the sine is positive, the angle is in the first or second quadrant.
\n" ); document.write( "if the sine is negative, the angle is in the third or fourth quadrant.
\n" ); document.write( "if the cosine is positive, the angle is in the first or fourth quadrant.
\n" ); document.write( "if the cosine is negative, the angle is in the second or third quadrant.
\n" ); document.write( "if the tangent is positive, the angle is in the first or third quadrant.
\n" ); document.write( "if the tangent is negative, the angle is in the second or fourth quadrant.
\n" ); document.write( "here's another reference that might be helpful.
\n" ); document.write( "https://www.purplemath.com/modules/quadangs2.htm \n" ); document.write( "

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