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Let's assume a right-angled triangle ABC with base AB = #5x# and hypotenuse AC = #7x#.

By Pythagoras theorem, we have: #BC^2 = AC^2 - AB^2#
BC is the perpendicular.
By definition, sin(t) is the ratio of the perpendicular to the hypotenuse of a right-angled triangle.
#sin t = sqrt(AC^2 - AB^2)/(AC)#
#implies sin(t) = sqrt(49x^2 - 25x^2)/(7x)#

Since the sine of any angle is a constant, irrespective of side lengths, we may assume #x# to be any number we wish. Let's assume it to be 1.
#implies sin t = sqrt(24)/7 = (2sqrt(6))/7#

(Note, we could have used the identity #sin^2x + cos^2x = 1# too)

The function cos(t) is symmetric about the y-axis. This means cos(-t) = cos(t)
#implies cos(-t) = -5/7#

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