Question 1161054


Each point lies on the terminal arm of an angle. Determine the six trigonometric ratios for the angle, rounded to four decimal places.

a) 

A({{{5}}}, {{{12}}})
=>{{{x=5}}} and {{{y=12}}}

find {{{r}}}

{{{r^2=x^2+y^2}}}

{{{r=sqrt(5^2+12^2)}}}

{{{r=sqrt(25+144)}}}

{{{r=sqrt(169)}}}

{{{r=13}}}

The six trigonometric functions are:

{{{sine(x) =y/r=12/13=0.9231}}}

{{{cos(x)=x/r=5/13=0.3846}}}

{{{tan(x)=y/x=12/5=2.4000}}}

{{{cot(x) =x/y=5/12=0.4167}}}

{{{sec(x)=r/x=13/5=2.6000}}}

{{{csc(x) =r/y=13/12=1.0833}}}


b) 

B({{{4}}}, {{{3}}})

=>{{{x=4}}} and {{{y=3}}}

find {{{r}}}

{{{r^2=x^2+y^2}}}

{{{r=sqrt(4^2+3^2)}}}

{{{r=sqrt(25)}}}
{{{r=5}}}

The six trigonometric functions are:

{{{sine(x) =y/r=3/5=0.6000}}}

{{{cos(x)=x/r=4/5=0.8000}}}

{{{tan(x)=y/x=3/4=0.7500}}}

{{{cot(x) =x/y=4/3=1.3333}}}

{{{sec(x)=r/x=5/4=1.2500}}}

{{{csc(x) =r/y=5/3=1.6667 }}}




d) 

D({{{7}}}, {{{24}}})

=>{{{x=7}}} and {{{y=24}}}

{{{r=sqrt(7^2+24^2)}}}

{{{r=sqrt(625)}}} 

{{{r=25}}} 

The six trigonometric functions are:

{{{sine(x) =y/r=24/25=0.9600}}}

{{{cos(x)=x/r=7/25=0.2800}}}

{{{tan(x)=y/x=24/7=3.4286}}}

{{{cot(x) =x/y=7/24=0.2917}}}

{{{sec(x)=r/x=25/7=3.5714}}}

{{{csc(x) =r/y=25/24=1.0417 }}}