Question
given that cos thiter = negative 3 /5,where 3.14 is less or equal to 3x3.14/2, find
1. sin thiter
2.tn thiter
1. sin thiter
2.tn thiter
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Answered by
GPT 3.5
1. Firstly we make use of the Pythagorean identity: sin^2(theta) = 1 - cos^2(theta)
Given that cos(theta) = -3/5, we can square it to find sin^2(theta):
sin^2(theta) = 1 - (-3/5)^2
sin^2(theta) = 1 - 9/25
sin^2(theta) = 16/25
Taking the square root of sin^2(theta) gives us sin(theta):
sin(theta) = ±4/5
However, since 3.14 ≤ (3x3.14)/2 ≤ 3.14/2, we know that the angle theta is in the second quadrant where sine is positive. Therefore, sin(theta) = 4/5.
2. To find the tan(theta), we know that tan(theta) = sin(theta) / cos(theta). We already know sin(theta) = 4/5 and cos(theta) = -3/5.
Therefore, tan(theta) = (4/5) / (-3/5)
tan(theta) = -4/3
Given that cos(theta) = -3/5, we can square it to find sin^2(theta):
sin^2(theta) = 1 - (-3/5)^2
sin^2(theta) = 1 - 9/25
sin^2(theta) = 16/25
Taking the square root of sin^2(theta) gives us sin(theta):
sin(theta) = ±4/5
However, since 3.14 ≤ (3x3.14)/2 ≤ 3.14/2, we know that the angle theta is in the second quadrant where sine is positive. Therefore, sin(theta) = 4/5.
2. To find the tan(theta), we know that tan(theta) = sin(theta) / cos(theta). We already know sin(theta) = 4/5 and cos(theta) = -3/5.
Therefore, tan(theta) = (4/5) / (-3/5)
tan(theta) = -4/3
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