Write the first expression in terms of the second if the terminal point determined by the t is in the given quadrant:
sin t, cos t; quadrant 2
sin^2 t = 1 - cos^2 t
sin t = +/- sqrt (1-cos^2 t)
in quadrant 2, sin t is + so use + sign
To determine the equivalence of the expressions in terms of the quadrant, we need to understand the trigonometric functions in each quadrant.
In quadrant 2:
- The sine function is positive (+).
- The cosine function is negative (-).
Given this information, we can rewrite the expression sin t in terms of cos t in quadrant 2:
sin t = sqrt(1 - cos^2 t)
In this case, since we know that t is in quadrant 2 and the cosine function is negative in quadrant 2, we can take the negative square root on the right side to match the given quadrant:
sin t = -sqrt(1 - cos^2 t)
Therefore, the expression sin t in terms of cos t in quadrant 2 is -sqrt(1 - cos^2 t).