document.write( "Question 949875: Find sin t and cos t for the given value of t.
\n" ); document.write( "t = −13π/4
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Algebra.Com's Answer #580009 by Theo(13342)\"\" \"About 
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if you use your calculator, you will get:
\n" ); document.write( "sin(-13*pi/4) =.7071067812
\n" ); document.write( "cos(-13*pi/4) = -.7071057812
\n" ); document.write( "your calculator should be in radian mode.
\n" ); document.write( "the fact that the answers are the same indicate the reference angle is probably 45 degrees since that only occurs when the reference angle is 45 degrees.
\n" ); document.write( "without use of the calculator, you would do the following.
\n" ); document.write( "since the angle is negative, keep adding 2*pi to it until it becomes positive.
\n" ); document.write( "2*pi is the same as 8*pi/4, so keep adding 8*pi/4 to -13*pi/3 until it becomes positive.
\n" ); document.write( "-13*pi/4 + 8*pi/4 = -5*pi/4 + 8*pi/4 = 3*pi/4.
\n" ); document.write( "your angle is now positive and is between 0 and 2*pi which is where you want it to be.
\n" ); document.write( "an angle of 3*pi/4 is between 2*pi/4 and 4*pi/4.
\n" ); document.write( "that puts the angle in the second quadrant.
\n" ); document.write( "the reference angle for an angle in the second quadrant is equal to pi - the angle.
\n" ); document.write( "pi is equal to 4*pi/4, so your reference angle is 4*pi/4 - 3*pi/4 which is equal to pi/4.
\n" ); document.write( "the reference angle is the equivalent angle in the first quadrant.
\n" ); document.write( "use your calculator to see that sin(pi/4) = .707... and cos(pi/4) = .707...
\n" ); document.write( "convert pi/4 to the equivalent angle in degrees and you can see that pi/4 * 180/pi is equal to 180*pi/4*pi which is equal to 45 degrees.
\n" ); document.write( "since you know that sine and cosine of 45 degrees is equal to sqrt(2)/2, then you can convert that to decimal form to see that it is equal to .7071......\r
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\n" ); document.write( "\n" ); document.write( "it is sometimes easier to convert the angle to degrees from the beginning.\r
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\n" ); document.write( "\n" ); document.write( "-13*pi/4 * 180/pi is equal to -585 degrees.
\n" ); document.write( "keep adding 360 until the angle is between 0 and 360.
\n" ); document.write( "-585 + 360 = -225 + 360 = 135.
\n" ); document.write( "135 is in the second quadrant.
\n" ); document.write( "reference angle is 180 - 135 = 45 degrees.
\n" ); document.write( "sine and cosine of 45 degrees is sqrt(2)/2.
\n" ); document.write( "that's in the first quadrant.
\n" ); document.write( "in the second quadrant, sine is positive and cosine is negative.
\n" ); document.write( "sin(135) is therefore equal to sqrt(2)/2.
\n" ); document.write( "cos(135) is therefore equal to - sqrt(2)/2.
\n" ); document.write( "the sine and cosine will be the same for every complete revolution around the unit circle.
\n" ); document.write( "135 - 360 = -225.
\n" ); document.write( "sin(-225) = sqrt(2)/2
\n" ); document.write( "cos(-225) = - sqrt(2)/2
\n" ); document.write( "-225-360 = -585
\n" ); document.write( "sin(-585) = sqrt(2)/2
\n" ); document.write( "cos(-585) = - sqrt(2)/2
\n" ); document.write( "you can use your calculator to confirm.
\n" ); document.write( "don't forget to set it to degrees is you're working with degrees.
\n" ); document.write( "also sqrt(2)/2 is equal to .7071067812 as indicated before.
\n" ); document.write( "your calculator will give you the decimal equivalent.\r
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