document.write( "Question 612346: Find the exact value of theta in degree (0° is less than or equal to theta<360°) and the remaining five trigonometric functions if cosine theta =negative square root of three divided by two and tangent theta<0 \n" ); document.write( "

Algebra.Com's Answer #385411 by jsmallt9(3758) $\"\"$ $\"About$

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We are given that cos and tan for theta are negative. cos is negative in the 2nd and 3rd quadrants. tan is negative in the 2nd and 4th quadrants. For both of them to be negative, theta must terminate in the 2nd quadrant.

\n" ); document.write( "Next we need to figure out the reference angle. We should recognize that $\"sqrt%283%29%2F2\"$ (Remember to ignore negatives when finding reference angles.) is a special angle value for cos. The special angle whose cos is $\"sqrt%283%29%2F2\"$ is 30 degrees.

\n" ); document.write( "So we want an angle that terminates in the 2nd quadrant with a reference angle of 30. And, according to the instructions, we want the angle to be between 0 and 360. There is only one such angle: 180-30 = 150 degrees. \n" ); document.write( "

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