Question

Consider angle C such that sin C= 7/25

Sketch a diagram to represent angle C in standard position if cos C is negative
Find the co-ordinates of a point P on the terminal arm of angle C.

Answer 1

You should have been told about the CAST rule, that is, an acronym telling you in which quadrants trig ratios are positive.
Since sinC is positive and cosC is negative
then C must be in quadrant II
since sinØ = opposite/hyptenuse
sinC = 7/25 --> y=7, r=25
x^2 + y^2= r^2
x^2 + 49 = 625
x^2 = 576
x = ±24, but we are in quad II, so x = -24

your terminal point is (-24,7)
join to the centre and finish the right-angled triangle

Answer 2

X^2 + Y^2 = C^2.
x^2 + 7^2 = 25^2,
x^2 = 25^2 - 7^2 = 576, x = 24.

If Cos C is negative, X is negative. Cos C = (-24)/25 = -0.96, C = 163.7o CCW from +x-axis. = 73.7o W. of N.

P(-24,7).