using trig ratios:
the height of the triangle (the y-value you are looking for) is given by: - sin(pi/3)
the base (the x-value you are searching for) is given by: cos(pi/3)
haha, there's one i never heard before! calling "theta" "data"2. Given sin data = -2/9 and tan data > 0, find cos data.
note that we are in the third quadrant, since sine is negative and tangent is positive. thus, we must have a negative value for cosine as well.
there are two ways to do this: by formula, or by trig/geometry
by formula: note that
as i said, here we want
just plug in the value for the sine and simplify
by trig/geometry. draw a right triangle. call an acute angle in the triangle . since sine of this angle is 2/9 (*), label the side opposite this angle 2 and label the hypotenuse 9. you can find the adjacent side by using Pythagoras' theorem. then you know cosine = adjacent/hypotenuse (and remember to put the minus sign at the end because we are in the third quadrant).
there's "data" again.3. Find the reference angle for data = -155
write the angle as a positive one.
this angle is between 180 and 270. when , the reference angle for is given by: . since we want the angle between and the x-axis
*) i am considering positive numbers here, we'll worry about negatives at the end. since we know what quadrant the angle is in, we know to apply a negative sign to the answer we get