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if sinA =3/4, calculate tha cos A and tanA.
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if sinA =3/4, calculate tha cos A and tanA. Related: Intro - sin, cos...
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if sinA =3/4, calculate tha cos A and tanA. Related: Intro - sin, cos...
To calculate cos A, we can use the Pythagorean identity: sin^2 A + cos^2 A = 1.
Given sin A = 3/4, we can square both sides:
(sin A)^2 = (3/4)^2
sin^2 A = 9/16
Now we can substitute this value into the Pythagorean identity:
(9/16) + cos^2 A = 1
Rearranging the equation:
cos^2 A = 1 - 9/16
cos^2 A = 16/16 - 9/16
cos^2 A = 7/16
Taking the square root of both sides, we find:
cos A = ±√(7/16)
Since cos A can be positive or negative, both √(7/16) and -√(7/16) are possible values for cos A.
To calculate tan A, we can use the formula:
tan A = sin A / cos A
Substituting the given value for sin A and the possible values for cos A:
tan A = (3/4) / (√(7/16)) = (3/4) * (√(16/7)) = (3/4) * (4/√7) = 3/√7 = (3√7) / 7
Similarly, tan A = (3/4) / (-√(7/16)) = (3/4) * (-4/√7) = -3/√7 = -(3√7) / 7
Therefore, tan A = (3√7) / 7 or -(3√7) / 7.
Given sin A = 3/4, we can square both sides:
(sin A)^2 = (3/4)^2
sin^2 A = 9/16
Now we can substitute this value into the Pythagorean identity:
(9/16) + cos^2 A = 1
Rearranging the equation:
cos^2 A = 1 - 9/16
cos^2 A = 16/16 - 9/16
cos^2 A = 7/16
Taking the square root of both sides, we find:
cos A = ±√(7/16)
Since cos A can be positive or negative, both √(7/16) and -√(7/16) are possible values for cos A.
To calculate tan A, we can use the formula:
tan A = sin A / cos A
Substituting the given value for sin A and the possible values for cos A:
tan A = (3/4) / (√(7/16)) = (3/4) * (√(16/7)) = (3/4) * (4/√7) = 3/√7 = (3√7) / 7
Similarly, tan A = (3/4) / (-√(7/16)) = (3/4) * (-4/√7) = -3/√7 = -(3√7) / 7
Therefore, tan A = (3√7) / 7 or -(3√7) / 7.
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if sinA =3/4, calculate tha cos A and tanA. Related: Intro - sin, cos & tan - Introduction to Trignometry
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