Evaluate the following expressions. The answer must be given as a fraction; NO DECIMALS. If the answer involves a square root it should be entered as sqrt . For instance, the square root of 2 should be written as sqrt(2).
If tan(o)=9/7 abd sin(o)

Question

Evaluate the following expressions. The answer must be given as a fraction; NO DECIMALS. If the answer involves a square root it should be entered as sqrt . For instance, the square root of 2 should be written as sqrt(2).  
If tan(o)=9/7 abd sin(o)<0 then find

sin(o)=
cos(o)=
sec(o)=
csc(o)=
cot(o)=

dumbcow · Answer

use Trig Identities and Pythagorean Theorem

cot = 1/tan = 7/9

sec^2 = 1+tan^2 = 1 + (81/49) = 130/49
--> sec = sqrt(130)/7

sec = 1/cos --> cos = 1/sec = 7/sqrt(130) = 7sqrt(130)/130

cos^2 = 1- sin^2 = 49/130
sin^2 = 1 - 49/130 = 81/130
 sin = 9/sqrt(130) = 9sqrt(130)/130