SOLUTION: tan theta=2 find the five other trigonometric function values

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Question 894134: tan theta=2 find the five other trigonometric function values
Found 2 solutions by Theo, Edwin McCravy:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
tan(theta) = 2
this means that opposite divided by adjacent is equal to 2.
this can occur if opposite = 2 and adjacent = 1
this would make hypotenuse equal to sqrt(2^2 + 1^2) = sqrt(5).
your other functions would then be:

sin (theta) = opp/hyp = 2/sqrt(5) = 2*sqrt(5)/5

cos(theta) = adj/hyp = 1/sqrt(5) = sqrt(5)/5

tan(theta) = opp/adj = 2/1 = 2

cot(theta) = adj/opp = 1/2

sec(theta) = hyp/adj = sqrt(5)/1 = sqrt(5)

csc(theta) = hyp/opp = sqrt(5)/2


Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

The other tutor assumed you meant only the first quadrant. But
the tangent is positive in both the first and the third quadrants.

tan%28theta%29=2

Two cases.  theta is in quadrant 1, and quadrant 3

Case 1, the only one the other tutor considered):

tan%28theta%29=y%2Fx=2%2F1

so take y=2, x=1

r=sqrt%28x%5E2%2By%5E2%29=sqrt%281%5E2%2B2%5E2%29=sqrt%281%2B4%29=sqrt%285%29

sin%28theta%29=y%2Fr=2%2Fsqrt%285%29=2sqrt%285%29%2F5

cos%28theta%29=x%2Fr=1%2Fsqrt%285%29=sqrt%285%29%2F5

cot%28theta%29=x%2Fy=1%2F2

sec%28theta%29=r%2Fx=sqrt%285%29%2F1=sqrt%285%29

Case 2:

tan%28theta%29=y%2Fx=%28-2%29%2F%28-1%29

so take y=-2, x=-1

r=sqrt%28x%5E2%2By%5E2%29=sqrt%28%28-1%29%5E2%2B%28-2%29%5E2%29=sqrt%281%2B4%29=sqrt%285%29

sin%28theta%29=y%2Fr=%28-2%29%2Fsqrt%285%29=-2sqrt%285%29%2F5

cos%28theta%29=x%2Fr=%28-1%29%2Fsqrt%285%29=-sqrt%285%29%2F5

cot%28theta%29=x%2Fy=%28-1%29%2F%28-2%29=1%2F2

sec%28theta%29=r%2Fx=sqrt%285%29%2F%28-1%29=-sqrt%285%29

Edwin