SOLUTION: determine the specified trigonometric ratio for each angle with a terminal side that passes through the given point. 1.Sin0; (-8,6) 2.csc0; (2,-1) 3.tan0;(0,1) 4.cos0; (-4,-

Question 1158028: determine the specified trigonometric ratio for each angle with a terminal side that passes through the given point.
1.Sin0; (-8,6)
2.csc0; (2,-1)
3.tan0;(0,1)
4.cos0; (-4,-2)
Answer by KMST(5377) (Show Source): You can put this solution on YOUR website!
The standard position of an angle is vertex at the origin, initial side along the positive x-axis.
We measure angles counterclockwise, and could define an angle measure as negative or greater than 360 degree,
but the trigonometric functions only care about the position of the terminal side.
I will assume for all angles.

Terminal side passing through :
There is a large right triangles with hypotenuse and a similar triangle whose hypotenuse, , is a radius of the unit circle shown in red.
The large one has legs of length and , and hypotenuse . The length of the small right triangle's hypotenuse, } ,is 10 times smaller, and so are the legs.
The function is defined as the y-coordinate of point A, , and is defined as the x-coordinate of point A, .
We can calculate as a trigonometric ratio. and determine that .

Trigonometric cosine and sine functions of , defined as the x-coordinate and the y-coordinate of point A respectively are numerically the same as those for , but may be positive or negative depending on the quadrant.
The sign will be the same for coordinates of any point on the terminal side.

Terminal side passing through :
is in quadrant IV, with positive x-coordinate, so .
The large right triangle, in this case, has leg lengths of 2, and 1, and a hypotenuse length of .
and (rounded)
The angles involved would be ,

Terminal side passing through :
P is on the unit circle, so its x-coordinate and y-coordinate are and respectively.
, and is undefined.

Terminal side passing through :
Booth coordinates are negative, and so will be sine and cosine.
OP would be the hypotenuse of a right triangle with leg lengths 4, and 2.
The hypotenuse length is

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