The terminal side of θ lies on given line in the specific quadrant. Find the values of the six trigonometric functions of θ by finding a point on the line.
Line : 4x + 3y = 0
Quadrant: IV
please show work. thanks
Line : 4x + 3y = 0
Quadrant: IV
please show work. thanks
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Consider point: 3,-4 on the given line, then:
sin θ = -4/5
cos θ = 3/5
tan θ = -4/3
For sec, cosec and cotan just invert these appropriately; e.g. cosec = 1/sin = -5/4
sin θ = -4/5
cos θ = 3/5
tan θ = -4/3
For sec, cosec and cotan just invert these appropriately; e.g. cosec = 1/sin = -5/4
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Did you sketch this line?
Do that and find the coordinates (x1, y1) of any point P on the line in the fourth quadrant (i.e. x1 positive and y1 negative)
(Hint: x = 3 makes it easy to find y.)
Then use Pythagoras' to find the distance of P from (0, 0);
call this distance r.
Then your six answers are (using the values you have for x, y, r)
sinθ = y/r
cosθ = x/r
tanθ = y/x
secθ = r/x
cosecθ = r/y
cotθ = x/y
Do that and find the coordinates (x1, y1) of any point P on the line in the fourth quadrant (i.e. x1 positive and y1 negative)
(Hint: x = 3 makes it easy to find y.)
Then use Pythagoras' to find the distance of P from (0, 0);
call this distance r.
Then your six answers are (using the values you have for x, y, r)
sinθ = y/r
cosθ = x/r
tanθ = y/x
secθ = r/x
cosecθ = r/y
cotθ = x/y