Question

let (-6,5) be a point on the terminal side of theta. find the exact values of sintheta, costheta, and sintheta

Answer 1

Given:

The point is (-6,5).

It is on the terminal side of theta.

To find:

The values of
`\sin\theta` and
`\cos \theta`.

Solution:

In the point (-6,5),

x-coordinate : x=-6

y-coordinate : y=5

So,
`r=√(x^2+y^2)`

`r=√((-6)^2+(5)^2)`

`r=√(36+25)`

`r=√(61)`

Now,

`\sin \theta=(y)/(r)`

`\sin \theta=(5)/(√(61))`

`\cos \theta=(x)/(r)`

`\cos \theta=(-6)/(√(61))`

Therefore, the required values are
`\sin \theta=(5)/(√(61))` and
`\cos \theta=-(6)/(√(61))`.