SP #7 Unit Q Concept 2

This post was made in collaboration with Carlos Rendon, view other awesome math posts on his blog here

In our problem, we are given the information that sin<1 and also that cot is equal to -1/3
-Our first step was to find tan becasue we already have cot and we only have to do the reciprocal in order to get this. Our answer is -3 as shown in the picture below
-Now that we have tan, we can use the pythagorean identity 1 +tan ^2 = sec^2 so sec^2 is 1+ (9), radical 10
-We have sec so we can do the reciprocal in order to find cos, it is radical 10/ 10
-To find sin we can do 1- cos^2 and get 9/10, after we take the reciprocal and rationalize we should get 3 radical 10/ 10
-And to find csc we do the reciprocal of sin and get radical 10/ 3


                                                                     

In order to solve this using SohCahToa,
-We know sin is y/r which is 3/rad 10 and then it becomes 3rad 10/ 10 after we rationalize
-for csc it's r/y and it is rad10/ 3
- cos is x/r which is rad 10/10
-To get sec it's r/x and we get radical 10
-Next is tan, y/x which is -3
-And to get x/y (cot) it will be -1/3