Question

Find sinif cos 0 =OAOB.OC.-252√5OD-Reset Selectionis in the fourth quadrant.

Answer 1

Rememeber that:

`cos\theta=(c.a)/(h)=\frac{\sqrt[\placeholder{⬚}]{5}}{5}`

In this case, c.a= square root(5) and h= 5.

using Pythagorean theorem, we will find the opposite leg:

`\begin{gathered} h^2=c.a^2+c.o^2 \\ c.o^2=h^2-c.a^2 \\ c.o=\sqrt[\placeholder{⬚}]{h^2-c.a^2}=\sqrt[\placeholder{⬚}]{5^2-(\sqrt[\placeholder{⬚}]{5})^2}=2\sqrt[\placeholder{⬚}]{5} \end{gathered}`

The sin of theta is given by:

`sin\theta=(c.o)/(h)=\frac{2\sqrt[\placeholder{⬚}]{5}}{5}`

And now, given that the angle is in the four quadrant.

As you can see the graph, the opposite cateto is negative, therefore:

`sin\theta=(-c.o)/(h)=\frac{-2\sqrt[\placeholder{⬚}]{5}}{5}`

The answer is: C.