Question

How do I solve this question?

Answer 1

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`