Question

Question #76773

Answer 1

1. `3131/3744~~0.8363`
2. `181/60~~3.017`

Explanation:

You are given that `cos(A)=5/13`. That is, for a triangle, the adjacent, "adj", angle is `5` and the hypotenuse, "hyp", is `13`.

Using the Pythagorean Theorem, you can get the opposite side

`"adjacent"^2+"opposite"^2="hypotenuse"^2`

`(5)^2+"opposite"^2=(13)^2`

`25+"opp"^2=169`

`"opp"^2=144`

`"opp"=12`

Using the right-triangle rules of trigonometric functions we have:

`sin(A)=("opp")/("hyp")=12/13`
`cos(A)=("adj")/("hyp")=5/13`
`tan(A)=("opp")/("adj")=12/5`
`csc(A)=("hyp")/("opp")=13/12`
`sec(A)=("hyp")/("adj")=13/5`
`cot(A)=("adj")/("opp")=5/12`

Plug these values into the first question:

`sin(A)-cot(A)/(2tan(A))=12/13-(5/12)/(2xx12/5)=12/13-5/12xx5/24`

`=12/13-25/288=3131/3744~~0.8363`

Finally, plug our values into the second question:

`cot(A)+1/(cos(A))=5/12+1/(5/13)=5/12+13/5=181/60~~3.017`