given that 180¡ã¡ÜA¡Ü 270¡ãand tan A=3/7,
what is the exact value of cos A?
can someone please help ???i need to know how to solve it !
thanks!
On my screen, it is symbols gone mad, I can't decipher your meaning. Can you type it in standard ASCII?
common symbols > greater than
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"given that 180¡ã¡ÜA¡Ü 270¡ãand tan A=3/7,
what is the exact value of cos A? "
where you saying something like
given that 180º < A < 270º and tan A=3/7,
what is the exact value of cos A?
if so, then consider a right-angled triangle with a vertical of 3 and a horizontal of 7 in the first quadrant, angle A at the origin.
then clearly tan A = 3/7
by Pythagoras the hypotenuse is √(3^2 + 7^2)
=√58
then cos A = 7/√58 if the angle is in the first quadrant
but your angle is in the third quadrant, where the cosine is negative
So the exact value of cos A = -7/√58
thanks!
To find the exact value of cos A, we need to remember the trigonometric identity:
cos² A + sin² A = 1
Since we know the value of tan A (which is equal to sin A / cos A), we can use this information to find the values of sin² A and cos² A.
We are given that tan A = 3/7, so sin A / cos A = 3/7.
By cross-multiplication, we have sin A = 3k and cos A = 7k, where k is a constant.
Now, we can substitute the values of sin A and cos A into the trigonometric identity:
(7k)² + (3k)² = 1
49k² + 9k² = 1
58k² = 1
k² = 1/58
Taking the square root of both sides, we find:
k = ±sqrt(1/58) = ±1 / sqrt(58)
Since A is an angle in the second quadrant (180° ≤ A ≤ 270°), cos A is negative. Therefore, we take the negative value of k:
k = -1/sqrt(58)
Now we can substitute this value back into cos A:
cos A = 7k = 7 * (-1/sqrt(58)) = -7/sqrt(58)
Thus, the exact value of cos A is -7/sqrt(58).