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steposvetlana [31]
3 years ago
6

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

Mathematics
2 answers:
Gnom [1K]3 years ago
7 0
30 is the answer of the question good luck
nydimaria [60]3 years ago
3 0
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}
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