Determine sina and cosa if cota=3. a belongs to (0;pi) Solution The interval (0,pi) covers the first and the second quadrant where the values of the sine function are positive. The cosine function is positive over the first quadrant, but it\'s negative in the second quadrant. We\'ll use the fundamental formula of trigonometry: (sin a)^2 + (cos a)^2=1 We\'ll divide the formula with the value (sin a)^2: (sin a)^2/ (sin a)^2 + (cos a)^2/(sin a)^2 = 1 / (sin a)^2 But the ratio cos a/sin a= cot a = 3 The formula will become: 1 + (cot a)^2 = 1/(sin a)^2 sin a = 1/sqrt[1+(cot a)^2] sin a = 1/sqrt[1+(3)^2] sin a = 1/sqrt[1+(3)^2] sin a = 1/sqrt[1+9] sin a = 1/sqrt 10 sin a = sqrt 10/10 cos a = +/- sqrt (1 - 1/10) cos a = +/- sqrt (9/10) cos a = +/- 3/sqrt 10 cos a = +/- (3*sqrt 10)/10.

1. Determine the elements of the set S
The elements have the property |x-1|=<4 . The elements are in Z set.
Solution
S = {x: |x-1| + < 4 and the elements are in z(or integers.)
To find the elements of S.
|x-1| =< 4
So,
-4 <= x-1 =< 4. Add 1.
-4+1 < = x =< 4+1
-3 <= x =< 5. Since x is also integer, therefore S = {-3,-2,-1,-0, 1,2,3,4,5}