Fundamental Trigonometric Ratios

1) Sin\theta = \frac{{perpendicular}}{{hypotenuse}} = \frac{y}{r}
2) Cos\theta = \frac{{base}}{{hypotenuse}} = \frac{x}{r}
3) Tan\theta = \frac{{perpendicular}}{{base}} = \frac{y}{x} = \frac{{Sin\theta }}{{Cos\theta }}
4) Cot\theta = \frac{{base}}{{perpendicular}} = \frac{x}{y} = \frac{{Cos\theta }}{{Sin\theta }}
5) Sec\theta = \frac{{hypotenuse}}{{base}} = \frac{r}{x} = \frac{1}{{Cos\theta }}
6) Co\sec \theta = \frac{{hypotenuse}}{{perpendicular}} = \frac{r}{y} = \frac{1}{{Sin\theta }}
7) Signs of trigonometric ratios
I QUADRANT: A means all trigonometric ratios are positive.
II QUADRANT: S means Sin and Co\sec are positive and all others are negative.
III QUADRANT: T means Tan and Cot are positive and all others are negative.
IV QUADRANT: C means Cos and Sec are positive and all others are negative.
NOTE: (1) Clockwise we read ACTS
(2) Counterclockwise we read ASTC (All Silver Tea Cups)
\theta in Quadrant
Sin\theta
Cos\theta
Tan\theta
Cot\theta
Sec\theta
Co\sec \theta
I
 +
 +
 +
 +
 +
 +
II
 +
 -
 -
 -
 -
 +
III
 -
 -
 +
 +
 -
 -
IV
 -
 +
 -
 -
 +
 -
8) Trigonometric Ratios of Special Angles:
\theta
Sin\theta
Cos\theta
Tan\theta
Cot\theta
Sec\theta
Co\sec \theta
{0^ \circ }
0
1
0
\infty
1
\infty
{30^ \circ }
\frac{1}{2}
\frac{{\sqrt 3 }}{2}
\frac{1}{{\sqrt 3 }}
\sqrt 3
\frac{2}{{\sqrt 3 }}
2
{45^ \circ }
\frac{1}{{\sqrt 2 }}
\frac{1}{{\sqrt 2 }}
1
1
\sqrt 2
\sqrt 2
{60^ \circ }
\frac{{\sqrt 3 }}{2}
\frac{1}{2}
\sqrt 3
\frac{1}{{\sqrt 3 }}
2
\frac{2}{{\sqrt 3 }}
{90^ \circ }
1
0
\infty
0
\infty
1
RULE: Write 0,1,2,3,4, divide by 4 and then take square roots and write the resulting number in the column of Sin\theta .