Question 1127757: Find all six trigonometric functions of θ if the given point is on the terminal side of θ. (If an answer is undefined, enter UNDEFINED.)
(−1, −3)
Found 2 solutions by Alan3354, HelloWOrld_iAmcoMing :
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! (-1,-3)
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x = -1, y = -3
r = sqrt(x^2 + y^2) = sqrt(10)
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sin = y/r
cos = x/r
tan = y/x
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cot = 1/tan
sec = 1/cos
csc = 1/sin
Answer by HelloWOrld_iAmcoMing (1)  (Show Source):
You can put this solution on YOUR website! So, 1st of all, we need to find the hypotenuse (r) by Pythagorean theorem since we now have already have x and y as -1 and -3.
so we have: x^2 + y^2 = r^2
(-1)^2 + (-3)^2 = r^2
1 + 9 = 10 = r^2
+√10 = r
Now, we have x=-1, y=-3, r= √10
=> sin(θ)= y/r = -3/√10 = -3√10/10
cos(θ)= x/r = -1/√10 = -1√10/10
tan(θ)= y/x = -3/-1 = 3
csc(θ)= r/y = -√10/3
sec(θ)= r/x = -√10
tan(θ)= x/y = -1/-3 = 1/3
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