Apply Pythagorean Theorem and find the missing value..
Where x being the adjacent side, y being the opposite side, and r is the hypotenuse.
Now that you got the values of x, y, and r, simply replace it in the 6 trigonometric ratios.
For each pair of values of sin(`theta) and cos(`theta), find the exact values of the four remaining trigonometric functions, when this is possible; otherwise find the four remianing functions to 3 significant figures:
sin(`theta)= 3/5, cos(`theta)= -4/5
sin(`theta)= .9170001, cos(`theta)= 3.98
Let us do them in another way.
sin(`theta)= 3/5, cos(`theta)= -4/5
That means for angle theta,
opposite sde ...(opp)... = 3
hypotenuse.....(hyp)... = 5
adjacent side ..(adj)... = -4
So,
tan(theta) = opp/adj = 3/(-4) = -3/4
cot(theta) = adj/opp = (-4)/3 = -4/3
sec(theta) = hyp/adj = 5/(-4) = -5/4
csc(theta) = hyp/opp = 5/3
--------------------------------
sin(`theta)= .9170001, cos(`theta)= 3.98
That means for angle theta,
opposite sde ...(opp)... = 0.9170001
hypotenuse.....(hyp)... = 1
adjacent side ..(adj)... = 3.98
So,
tan(theta) = opp/adj = 0.9170001 /3.98 = 0.2304
cot(theta) = adj/opp = 3.98 /0.9170001 = 4.34024
sec(theta) = hyp/adj = 1 /3.98 = 0.25126
csc(theta) = hyp/opp = 1 /0.9170001 = 1.09051