The point (x,y) = (-1,5) is located in the second quadrant. So it's best to draw the point on your xy-coordinate plane and draw a line segment to the origin (0,0).
Then drop a line from (-1,5) straight down to the x-axis. What you should have is a right triangle with the following coordinates: (0,0); (-1,5); (-1,0).
If you look at the right triangle, you will have the small leg on the x-axis. It's length is 1 unit. The larger leg will be 5 units long. The length of the hypoteneuse can be calculated using the Pythagorean Theorem. c2 = a2 + b2, where the hypoteneuse c, has a length of √26.
In summary:
- short leg length = 1 unit
- long leg length = 5 units
- hypoteneuse length = √26 units
Let x be the length of the leg on the x-axis (short leg).
Let y be the length of the other leg (long leg).
Let r be the length of the hypoteneuse.
x = -1
y = 5
r = √26
Now we can calculate our trigonometric identities:
sin θ = y/r
cos θ = x/r
tan θ = y/x
cot θ = x/y
sec θ = r/x
csc θ = r/y
