To find the tangent of an angle when the sine is 3/4, we can use the following identity:
tan(theta) = sin(theta) / cos(theta)
Given that sin(theta) = 3/4, we can use the Pythagorean identity to find cos(theta):
cos(theta) = sqrt(1 - sin(theta)^2)cos(theta) = sqrt(1 - (3/4)^2)cos(theta) = sqrt(1 - 9/16)cos(theta) = sqrt(7/16)cos(theta) = sqrt(7) / 4
Now, we can substitute sin(theta) and cos(theta) into the tangent formula:
tan(theta) = (3/4) / (sqrt(7) / 4)tan(theta) = 3/sqrt(7)
Therefore, the tangent of the angle theta when sin(theta) = 3/4 is 3/sqrt(7).
To find the tangent of an angle when the sine is 3/4, we can use the following identity:
tan(theta) = sin(theta) / cos(theta)
Given that sin(theta) = 3/4, we can use the Pythagorean identity to find cos(theta):
cos(theta) = sqrt(1 - sin(theta)^2)
cos(theta) = sqrt(1 - (3/4)^2)
cos(theta) = sqrt(1 - 9/16)
cos(theta) = sqrt(7/16)
cos(theta) = sqrt(7) / 4
Now, we can substitute sin(theta) and cos(theta) into the tangent formula:
tan(theta) = (3/4) / (sqrt(7) / 4)
tan(theta) = 3/sqrt(7)
Therefore, the tangent of the angle theta when sin(theta) = 3/4 is 3/sqrt(7).