Question

sec theta = -4√7/7
Find sin(2theta) if cdc theta is greater than 0

Answer 1

hi

Answer 2

draw a triangle, make the hypotenuse \(4\sqrt7\) and the adjacent side \(7\)

Answer 3

all that is missing is \(b\) which you find by pythagoras
\[b=\sqrt{(4\sqrt{7})^2-7^2}=\sqrt{63}\]

Answer 4

now you can take any trig ratio you want

Answer 5

ooh you want
\[\sin(2\theta)\]

Answer 6

that is
\[2\sin(\theta)\cos(\theta)\] we can find it in a second

Answer 7

Thank you!

Answer 8

but first what does cdc theta is greater than 0
mean?

Answer 9

anyways
\[\cos(\theta)=-\frac{7}{4\sqrt7}\] and
\[\sin(\theta)=\frac{\sqrt{63}}{4\sqrt{7}}\]

Answer 10

plug them in above and see what you get when you simplify
\[2\times -\frac{7}{4\sqrt7}\times \frac{\sqrt{63}}{4\sqrt{7}}\]

Answer 11

how did you get sqrt 63?