Question

if cos(t) = 2/3 and t is in the fourth quadrant, then evaluate sin(6pi + t).

Answer 1

should i square cos and find its sin value and then use the sin(pi + t) = -sin t? :o

Answer 2

6pi is 3 complete rotations back to the 4th quadrant. We know that sine is negative in that quadrant. From the 2/3 we know that adj/hyp = 2/3. So we can use pythagoreans:
\[3^2-2^2=opp^2\]
\[9-4=5\]
\[opp=\sqrt{5}\]
From the definition of sine and knowing that sine is negative we have:
\[sin\theta=-\frac{\sqrt{5}}{3}\]

Answer 3

Clear as mud?

Answer 4

yes it makes sense. thank you : )

Answer 5

Happy to help. Keep the signs clear in your head when approaching these problems and view it from a reference angle perspective.

Answer 6

Okay : D