Question

CotA =5/12then sinA+cosa=?

Answer 1

`sinA+cosA=17/13`

Explanation:

`cotA=5/12`
cotangent= adjecent/opposite
thus the hypotenuse is:
`h=sqrt(25+144)=13`
`sinA=12/13`
`cosA=5/13`
`sinA+cosA=12/13+5/13=17/13`

Answer 2

`sin A + cos A = +- 17/13`

Explanation:

Use trig identities to find sin A and cos A
`cos^2 A = 1/(1 + tan^2 A) = 1/(1 + 25/144) = 144/169`
`cos A = +- 12/13`
`cot A = 5/12` --> A could be in Q. 1 or Q. 3.
`sin^2 A = 1 - cos^2 A = 1 - 144/169 = 25/169`
`sin A = +- 5/13`
If A is in Quadrant 1 -->
`sin A + cos A = 12/13 + 5/13 = 17/13`
If A is in Quadrant 3 -->
`sin A + cos A = - 12/13 - 5/13 = - 17/13`
Answer: `sin A + cos A = +- 17/13`