If sin 0 = -3 / 5 and pi < 0 < 3pi / 2, then tan 0 = ?
F. -5 / 4
G. -3 / 4
H. -3 / 5
J. 3 / 4
K. 4 / 5
since sinØ = opposite/hypotenuse = -3/5
you should recognize the 3-4-5 right-angled triangle.
You are also told the the angle (or triangle) is in the I, II, or IIIrd quadrant.
But isn't sinØ negative only in III of those given?
so x = -4, y= -3
thus tanØ = y/x = opposite/adjacent = -3/-4 = 3/4
Follow this type of reasoning for all of these kind of questions, and they become very very easy.
To find the value of tan(0), we need to know the value of sin(0).
Given that sin(0) = -3/5, we can use the identity: tan(x) = sin(x) / cos(x).
To find the value of cos(0), we can use the Pythagorean identity: sin^2(x) + cos^2(x) = 1.
Substituting the value of sin(0) into the equation, we can solve for cos(0):
(-3/5)^2 + cos^2(0) = 1
9/25 + cos^2(0) = 1
cos^2(0) = 1 - 9/25
cos^2(0) = (25 - 9)/25
cos^2(0) = 16/25
cos(0) = ±√(16/25)
cos(0) = ±(4/5)
Since we know that pi < 0 < 3pi/2, we know that 0 is in the second quadrant where the cosine is negative.
Therefore, cos(0) = -4/5.
Now, we can find the value of tan(0):
tan(0) = sin(0) / cos(0)
tan(0) = (-3/5) / (-4/5)
tan(0) = 3/4
Therefore, the value of tan(0) is 3/4.
The correct answer is J. 3/4.
To find the value of tan 0, we can use the relationship between sine and cosine: tan 0 = sin 0 / cos 0.
Given that sin 0 = -3 / 5, we need to find cos 0.
Since pi < 0 < 3pi / 2, it lies in the third quadrant of the unit circle, where both sine and cosine are negative.
Using the Pythagorean identity, we can find cos 0:
sin^2 0 + cos^2 0 = 1
(-3 / 5)^2 + cos^2 0 = 1
9 / 25 + cos^2 0 = 1
cos^2 0 = 1 - 9 / 25
cos^2 0 = 16 / 25
cos 0 = -4 / 5
Now, substitute these values into the tan 0 formula:
tan 0 = sin 0 / cos 0
tan 0 = (-3 / 5) / (-4 / 5)
tan 0 = -3 / 5 * -5 / 4
tan 0 = 3 / 4
Therefore, the value of tan 0 is 3 / 4, which corresponds to option J.