Question

If cosa = -4/5 with a in QIII. Find sin2a

Answer 1

30 is the answer of the question good luck

Answer 2

Since a is in the third quadrant, both sina and cosa are negative.

Now, sin(2a) can be rewritten as 2sin(a)cos(a).
Thus, we can find sin(a) by using Pythagoras' Theorem.

$cos(a) = -\frac{4}{5}$

Now, by focusing on the positive value, we can see that 5 is the hypotenuse.
Let the missing side be x.
x² + 16 = 25
x² = 9
x = 3, because x > 0

$\text{Thus, } sin(a) = -\frac{3}{5}$

Substituting these into the equation, we get:
$2sin(a) cos(a) = 2 \cdot -\frac{3}{5} \cdot -\frac{4}{5}$
$2sin(a) cos(a) = \frac{24}{25}$

$\therefore sin(2a) = \frac{24}{25}$