Answer:
See below.
Step-by-step explanation:
(i) Sin 130 = sin ( 180 - 130) = sin 50 = k (answer).
(ii) sin 50 = cos (90 - 50) = cos 40 = k.
The right angle with hypotenuse of 1 and the side opposite the angle whose sine is k has the adjacent side = √(1 - k^2) ( by the Pythagoras theorem),
so the sine of (90 - 50) = sin 40 = √(1 - k^2)/ 1.
Therefore tan 40 = sin 40 / cos 40 = √(1 - k^2) / k (answer)
(iii) cos ( -220) = cos (360 - 220) = cos 140 = - cos 40
= -k.
Now since sec x = 1 / cos x :
sec (-220) = -1/k (answer).
