2.1 If `sin(x)=1/2`, find other trigonometry functions `cos(x),tan(x),csc(x),sec(x),cot(x)`
Solution:
`sin(x)=1/2`
`cos^2(x)=1-sin^2(x)`
`=1-(1/2)^2`
`=1-1/4`
`=(4-1)/4`
`=3/4`
`:.cos(x)=1.73/2`
`csc(x)=1/sin(x)`
`=1/(1/2)`
`=2`
`sec(x)=1/cos(x)`
`=1/(1.73/2)`
`=2/1.73`
`tan(x)=sin(x)/cos(x)`
`=(1/2)/(1.73/2)`
`=1/1.73`
`cot(x)=1/tan(x)`
`=1/(1/1.73)`
`=1.73`
2.2 If `sin(x)=1/2`, solve `cos(x)csc(x)+tan(x)sec(x)`
Solution:
`sin(x)=1/2` (given)
`cos(x)csc(x)+tan(x)sec(x)=?`
`sin(x)=1/2`
`cos^2(x)=1-sin^2(x)`
`=1-(1/2)^2`
`=1-1/4`
`=(4-1)/4`
`=3/4`
`:.cos(x)=1.73/2`
`csc(x)=1/sin(x)`
`=1/(1/2)`
`=2`
`sec(x)=1/cos(x)`
`=1/(1.73/2)`
`=2/1.73`
`tan(x)=sin(x)/cos(x)`
`=(1/2)/(1.73/2)`
`=1/1.73`
Now substitute all these expression values in
`cos(x)csc(x)+tan(x)sec(x)`
`=(1.73/2)*(2)+(1/1.73)*(2/1.73)`
`=173/100+2/3`
`=12/5`
`:. cos(x)csc(x)+tan(x)sec(x)=12/5`
This material is intended as a summary. Use your textbook for detail explanation.
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