bashbobhash said:
Hi, I need to evaluate the trigonometric functions of Theta, given a line that the terminal side of theta lies on and the quadrant.
The instructions say:
The terminal side of theta lies on a given line in the specified quadrant. Find the values of the six trigonometric functions of theta by finding a point on the line.
The line: y = 1/3x
Quadrandt: III
So, I note that I need a point on the line and it should be in quadrant 3.
I came up with (-1, 5) and not quite sure what to do next. Any pointers would be greatly appreciated.
Hmmmm......the point (-1, 5) is NOT in quadrant III, and it is NOT on the line y = (1/3)x.
So, using the coordinates of that point, you're clearly not going to get the right values for the six trig functions.
You can certainly pick -1 as the value of x. To find the corresponding value of y, substitute -1 into the equation:
y = (1/3)x
y = (1/3)*(-1)
y = -1/3
The point (-1, -1/3) is in quadrant III and does lie on the line.
A little "forethought" might have suggested choosing a value of x which is a multiple of 3...why? Because to find y, you have to multiply (1/3)*x. Having integer values for both x and y will make the rest of your problem much easier.
Suppose we use -3 for x. If x = -3,
y = (1/3)(-3)
y = -1
The point (-3, -1) is in quadrant 3, and lies on the desired line.
Now....if I were doing this problem, I would use the definitions of the trig functions which involve x, y, and r:
sin A = y/r
cos A = x/r
tan A = y/x
csc A = r/y
sec A = r/x
cot A = x/y
r is the distance between the point (x, y) and the origin....you can determine the value of y using the distance formula.
r = sqrt(x^2 + y^2)
If x = -1 and y = -3, r = sqrt(10)
sin A = -3/sqrt(10)
etc.......
