Use identities to find the exact values at alpha for the remaining five trigonom
ID: 2878532 • Letter: U
Question
Use identities to find the exact values at alpha for the remaining five trigonometric functions. cos alpha = -Squareroot 2/9 and alpha is in quadrant III. sin alpha = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) cos alpha = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) sec alpha = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) tan alpha = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) cot alpha = ' (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)Explanation / Answer
In quadrant 3, only tan and cot are positive; rest sin, cos, sec, cosec are negative
cos a= - (20.5) /9;
sin a= sqrt (1- cos 2a) = sqrt (1- 2/81) = sqrt (79/81) = 790.5/ 9 but with a negative sign so sin a= - 790.5/9
tan a= sin a/ cos a = -(790.5 /9) / - (20.5 )/9 = sqrt(79/2)
cot a= 1/tan a= sqrt (2/79) ;
sec a= 1/ cos a = 1/ - (20.5) /9 = -9/ sqrt(2) ;
cosec a= 1/sin a = 1/ - 790.5/9 = -9/ sqrt(79)
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