SOLUTION: Hi
if sin theta is -4/9 and theta isin the 4th quadrant find the exact value of tan theta and sec theta.
could you please show your workings.
Thanks
You are given sin(t) = and "t" is in the 4-th quadrant.
In QIV cos(t) is positive, and therefore
cos(t) = = = = = = .
Then tan(t) = = = = rationalize the denominator = .
Next sec(t) = = = = rationalize the denominator = .
this means opposite side to the angle is -4 and hypotenuse is 9.
this forms a right triangle on the unit circle where x is the length of the adjacent side
and y is the length of the opposite side and h is the length of the hypotenuse.
sin(theta) = y/h
cos(theta) = x/h
tan(theta) = y/x
since it's a right triangle, then x^2 + y^2 = h^2.
this gets you x^2 + (-4)^2 = 9^2
this results in x^2 + 16 = 81
solve for x^2 to get x^2 = 81 - 16 = 65
solve for x to get x = sqrt(65)
you now have:
x = sqrt(65) = adjacent side
y = -4 = opposite side
h = 9 = hypotenuse