Given: ,
,
Find:
, . That's Q3
Draw the picture of angle A in the third quadrant Q3.
Since the cosine is adjacent/hypotenuse or x/r, and since we are given
, make x=-7 and r=, and calculate y using the
Pythagorean theorem:
x²+y² = r²
(-7)²+y² = 25²
49+y² = 625
y² = 576
y = ±√576
y = ±24, we take y = -24
We take y negative because it goes down from the x-axis,
and we ALWAYS take r positive because it begins on the
right side of the x-axis and doesn't change its sign when
it swings around into the other quadrants.
--------------------------------
, . That's Q4
Draw the picture of angle B in the fourth quadrant Q4. Since the sine is
opposite/hypotenuse or y/r, and since we are given ,
make y=-3 and r=5, and calculate x using the Pythagorean theorem:
x²+y² = r²
x²+(-3)² = 5²
x²+9 = 25
x² = 25
y = ±√25
y = ±5, we take y = -5
We take y negative because it goes down from the x-axis,
and we ALWAYS take r positive because it begins on the
right side of the x-axis and doesn't change its sign when
it swings around into the other quadrants.
-----------------------------------------------
--------------------------------------
---------------------------------------
Edwin