SOLUTION: If cos (0) = 5/11 and (0)is in quadrant IV, use an appropriate identify to compute the value of each of the following. a) tan(0) cot(0) b) csc(0) tan(0) c) sin^2(0)+cos^2

Algebra ->  Trigonometry-basics -> SOLUTION: If cos (0) = 5/11 and (0)is in quadrant IV, use an appropriate identify to compute the value of each of the following. a) tan(0) cot(0) b) csc(0) tan(0) c) sin^2(0)+cos^2      Log On


   

Question 826804: If cos (0) = 5/11 and (0)is in quadrant IV, use an appropriate identify to compute the value of each of the following.
a) tan(0) cot(0)
b) csc(0) tan(0)
c) sin^2(0)+cos^2(0)
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
a) tan(0) cot(0)
Since tan and cot are reciprocals of each other and since the product of reciprocals is always 1:
tan(0) cot(0) = 1

c) sin^2(0)+cos^2(0)
One of the Pythagorean identities tells us that this is 1:
sin^2(0)+cos^2(0) = 1

b) csc(0) tan(0)
This is the only one where we have to do a little work. One way, not the only way, to work with Trig expressions/equations is to use identities to rewrite the expression/equation in terms of sin's and/or cos's. Sometimes this makes the solution clearer. Replacing csc(0) with 1/sin(0) and tan(0) with sin(0)/cos(0) we get:
%281%2Fsin%28theta%29%29%28sin%28theta%29%2Fcos%28theta%29%29
The sin's cancel:
%281%2Fcross%28sin%28theta%29%29%29%28cross%28sin%28theta%29%29%2Fcos%28theta%29%29
leaving:
%281%2F1%29%281%2Fcos%28theta%29%29
which simplifies to:
1%2Fcos%28theta%29
Since we've been given the value for cos(0) we can substitute that in:
1%2F%285%2F11%29
which simplifies to:
11%2F5