How do you find the trig ratios by drawing the terminal and finding the reference angle: sin(235°)?
The terminal side of 235 degree angle lies in the IIIrd quadrant, hence the reference angle would be the smallest angle made with the x - axis.It would therefore be 235-180 =55 degrees.
To find the trignometrical ratio, construct any right triangle with the the terminal side of the given angle as the hypotenuse and x- axis as the base. Now, find the ratio of the measure of side opposite to to angle 55 and the hypotenuse. The sign of the measure of the side opposite to angle of 55, would be negative.
To be specific, the terminal side of the reference angle may be taken as the radius of unit circle. One end point of this radius, which would form the hypotenuse of the triangle referred to above, would be (0,0). Its length would be 1 unit (may be 1 cm or 1 inch). From the other end point draw a perpendicular on x axis. This would form the required right triangle. Measure its two sides and work out all the required trignometrical ratios for angle 235 degrees. The sign of the length of both sides would be negative.