Question

If point A(-5, -7) lies on the terminal arm of an angle, determine the exact value for the

primary trigonometric ratios of the angle.

Answer 1

`sin(a)=(y)/(r)=-(7√(74) )/(74)`

`cos(a)=(x)/(r) =-(5√(74) )/(74)`

`tan(a)=(y)/(x) =(7)/(5)`

Explanation:

Given the terminal side of an angle we can calculate the distance between the point given and the origin:

`r=√(x^2+y^2)`

`r=√(|(-5^2)+(-7^2)|)`

`r=√(74)`

y = opposite side

x = adjacent side

r = hypotenuse

Now we have

`r=√(74)`

`x=-5`

`y=-7`

`sin(a)=(y)/(r)=-(7√(74) )/(74)`

`cos(a)=(x)/(r) =-(5√(74) )/(74)`

`tan(a)=(y)/(x) =(7)/(5)`