given that 180¡ã¡ÜA¡Ü 270¡ãand tan A=3/7,

what is the exact value of cos A?

i can't get my head around this...can someone please help??
thanks!

To find the exact value of cos A, we can make use of the given information that tan A = 3/7 and the fact that 180° ≤ A ≤ 270°.

We know that tan A = opposite/adjacent, which means that the opposite side of angle A is 3 and the adjacent side is 7.

Now, let's visualize angle A in the third quadrant on the unit circle:
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In the third quadrant, the x-coordinate (adjacent side) is negative, and the y-coordinate (opposite side) is also negative. Since the adjacent side is -7 and the opposite side is -3, we can use the Pythagorean theorem to find the hypotenuse:

Hypotenuse^2 = (-7)^2 + (-3)^2
Hypotenuse^2 = 49 + 9
Hypotenuse^2 = 58
Hypotenuse = √58

Now, we know that cos A = adjacent/hypotenuse. Plugging in the values, we get:

cos A = (-7)/√58

To rationalize the denominator, we multiply the numerator and denominator by √58:

cos A = (-7 * √58)/(√58 * √58)
cos A = (-7√58)/(58)
cos A = -√58/8

Therefore, the exact value of cos A is -√58/8.