The terminal side of theta lies on a given line in the speci

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. Line Quadrant 2x - y = 0 III sin theta = _______ cos theta = _______ tan theta = _______ csc theta = _______ sec theta = _______ cot theta = _______

Solution

2x - y =0

y/x = 2 (i.e tan (theta) = opposite/hypotenus =2)

Then,

By pythogerous theorem,

Ac^2 =AB^2 +Bc^2

= (2)² + (1)² = 5

sin()= y/ r = 23

csc()= 1/ sin= 3/2

cos()= x/r = 13

sec()= 1/cos = 3

tan()=2

cot()= x/y = 1/ 2

Explanation:

Any relation of the form Ax+By=C has a slope of (i.e. a tan) AB
So 2xy=0 has a slope (tan) of 2.

Furthermore, we can see that 2xy=0 passes through the origin.