document.write( "Question 1203785: I'm so confused on what my math teacher is asking...
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\n" ); document.write( "I need to find θ but I don't understand how to solve for it. If you could show me how to do it or maybe even if possible show me some examples it would be greatly appreciated because I really want to try and solve the rest of the problems myself. :D \n" ); document.write( "
Algebra.Com's Answer #839650 by mccravyedwin(407)\"\" \"About 
You can put this solution on YOUR website!
\"sin%28theta%29=4%2F5\", \"cos%28theta%29=-3%2F5\"
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document.write( "You should memorize which trig ratios are positive and which ones are\r\n" );
document.write( "negative in which quadrants. \r\n" );
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document.write( "In QI, ALL 6 trig ratios are positive.\r\n" );
document.write( "In QII, Only the SINE and its reciprocal, the cosecant, are positive and the other 4 are negative.\r\n" );
document.write( "In QIII, Only the TANGENT and its reciprocal, the cotangent, are positive and the other 4 are negative.\r\n" );
document.write( "In QIV, Only the CALCULUS and its reciprocal, the secant, are positive and the other 4 are negative. \r\n" );
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document.write( "An easy mnemonic way to memorize this is to memorize this sentence for the\r\n" );
document.write( "basic 3 trig functions sine, cosine, and tangent.\r\n" );
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document.write( "ALL STUDENTS TAKE CALCULUS.\r\n" );
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document.write( "Back to your problem:\r\n" );
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document.write( "\"sin%28theta%29=4%2F5\", \"cos%28theta%29=-3%2F5\"\r\n" );
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document.write( "The sine, 4/5, is a POSITIVE number, so if you've memorized the above, you\r\n" );
document.write( "know that the sine is only positive in QI and QII\r\n" );
document.write( "The cosine, -3/5 is a NEGATIVE number, so if you've memorized the above, you\r\n" );
document.write( "know that the cosine is only positive in QI and QIV, so it is negative only in QII and QIII.\r\n" );
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document.write( "Therefore we know that θ is in QII. So we draw a right triangle in QII,\r\n" );
document.write( "with one side on the x axis. Angles are always measured counter-clockwise from\r\n" );
document.write( "the right side of the x-axis. So we draw an arc to indicate the angle θ.\r\n" );
document.write( "The x value is the adjacent side, the y-value is the opposite side, the r-value is the hypotenuse. \r\n" );
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document.write( "Angle θ is OUTSIDE the triangle and the reference angle is INSIDE the\r\n" );
document.write( "triangle, indicated in green by ref(θ).  We use only positive numbers to\r\n" );
document.write( "calculate the reference angle.\r\n" );
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document.write( "We find the value of the reference angle by calculator using ONLY POSITIVE\r\n" );
document.write( "NUMBERS. The sine of the reference angle is its opposite 4, over the\r\n" );
document.write( "hypotenuse 5. So on the TI-84, in degree mode, we press \r\n" );
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document.write( "2nd, sin, 4, ÷, 5, \r\n" );
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document.write( "We see this:\r\n" );
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document.write( "           \"53.13010235\"\r\n" );
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document.write( "So the reference angle is 53.13010235o.\r\n" );
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document.write( "The actual angle is measured by the red arc, so we subtract that value\r\n" );
document.write( "from 180o, and get 126.8698977o.\r\n" );
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document.write( "126.8698977o  <--answer\r\n" );
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document.write( "Edwin
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