Question

Let cosx =1/(sqrt 10) with x in QIV. Find sin2x

Answer 1

There is a "double angle formula" for the sine. Would you please look that up, either in your textbook or online. Copy down the formula for sin (2x).

Next, draw an angle in Q IV that has the cosine 1/Sqrt(10). Find the length of the opposite side.

Answer 2

Now, knowing sin theta and cos theta, write the formula for sin (2 theta).

Answer 3

x in Quadrant IV. <---- meaning, "adjacent side" is positive and "opposite side" is negative

Answer 4

RIght on, JD!

@smw1031 : Why not draw this angle as best you can, using the Draw utility, below? Doing so may make it easier for you to visualize what you're doing.

Answer 5

\(\bf cos(x)=\cfrac{1}{\sqrt{10}}\implies \cfrac{adjacent}{hypotenuse}\implies \cfrac{a=1}{c=\sqrt{10}}
\\ \quad \\
c^2=a^2+b^2\implies \pm\sqrt{c^2-a^2}={\color{blue}{ b}}\quad recall\quad sin(x)=\cfrac{{\color{blue}{ b}}}{c}
\\ \quad \\
\textit{IV quadrant, "b" is negative, thus }sin(x)=\cfrac{{\color{blue}{ -b}}}{c}
\\ \quad \\
\textit{keep in mind that }sin(2\theta)=2sin(\theta)cos(\theta)\)

Answer 6

Thanks everybody! I got -3/5. Sound right?

Answer 7

I got -3/5. Sound right? \(\huge \checkmark\)

Answer 8

Sweeeeeet!