ANGLES IN QUADRANTS

ANGLES IN QUADRANTS
The values of trigonometric ratios of 180⁰  If =180⁰, then op coincide ‘with ox’
    Let op = r = 1
    x = -1, y = 0  

\(sin{180^0} = \frac{y}{r} = \frac{0}{{ - 1}} = 0 = \,\,\,\,\, \Rightarrow \sin {180^0} = 0\) 
\(\cos {180^0} = \frac{x}{r} = \frac{{ - 1}}{1} = - 1 \Rightarrow \cos {180^0} = - 1\)           
\(\tan {180^0} = \frac{y}{x} = \frac{0}{{ - 1}} = 0 \Rightarrow \,\,\,\,\,\tan {180^0} = 0\)     
\(\csc {180^0} = \frac{r}{y} = \frac{{ + 1}}{0} = \infty \Rightarrow \,\,\,\,\,\csc {180^0} = \infty \)
 \(\sec {180^0} = \frac{r}{x} = \frac{1}{{ - 1}} = - 1 \Rightarrow \sec {180^0} = - 1\)
\(\cot {180^0} = \frac{x}{y} = \frac{{ - 1}}{0} = - \infty \Rightarrow \cot {180^0} = - \infty \)
The values of Trigonometric ratios of 270⁰  If =270⁰,then op coincide with  negative y -axis (oy’)
Let op = r =1; x = 0, y = -1 
 
\(sin\,\,{270^0} = \frac{y}{r} = \frac{{ - 1}}{1} = - 1\,\,\,\,\, \Rightarrow \sin \,{270^0} = - 1\)
\(\cos {270^0} = \frac{x}{r} = \frac{0}{1} = 0 \Rightarrow \cos {270^0} = 0\) 
\(\tan {270^0} = \frac{y}{x} = \frac{{ - 1}}{0} = - \infty \Rightarrow \,\,\,\,\,\tan {270^0} = - \infty \)   
\(\csc {270^0} = \frac{r}{y} = \frac{1}{{ - 1}} = - 1 \Rightarrow \,\,\,\,\,\csc {270^0} = - 1\)
\(\sec {270^0} = \frac{r}{x} = \frac{1}{0} = \infty \Rightarrow \sec {270^0} = \infty \)
\(\cot {270^0} = \frac{x}{y} = \frac{0}{{ - 1}} = 0 \Rightarrow \cot {270^0} = 0\)    
The Values of  Trigonometric ratios of 360⁰ 

If \(\theta\)=360⁰,then op coincide with positive y -axis
Let op = r = 1, x = 1, y = 0
\(\therefore sin{360^0} = \frac{y}{r} = \frac{0}{1} = 0\,\,\,\,\, \Rightarrow \sin {360^0} = 0\)
\(\cos {360^0} = \frac{x}{r} = \frac{1}{1} = 1 \Rightarrow \cos {360^0} = 1\)
\(\tan {360^0} = \frac{y}{x} = \frac{0}{1} = 0 \Rightarrow \,\,\,\,\,\tan {360^0} = 0\)
\(\csc {360^0} = \frac{r}{y} = \frac{1}{0} = \infty \Rightarrow \,\,\,\,\,\csc {360^0} = \infty \)
\(\sec {360^0} = \frac{r}{x} = \frac{1}{1} = 1 \Rightarrow \sec {360^0} = 1\)   
\(\cot {360^0} = \frac{x}{y} = \frac{1}{0} = \infty \Rightarrow \cot {360^0} = \infty \)