Question

Write the expression sin(t) in terms of cos(t) if the terminal point determined by t is in quadrant II.

Answer 1

To express sin(t) in terms of cos(t) for quadrant II, we use the positive root of the Pythagorean identity: sin(t) = √(1 - cos^2(t)), since sin is positive and cos is negative in quadrant II.

Step-by-step explanation:

To write the expression sin(t) in terms of cos(t) when the terminal point determined by t is in quadrant II, we can use the Pythagorean identity for sine and cosine which states that:

sin2(t) + cos2(t) = 1

In quadrant II, the sine function is positive and the cosine function is negative. Therefore, if we solve the Pythagorean identity for sin(t):

sin(t) = ±√(1 - cos2(t))

Because we're in quadrant II where sin(t) is positive:

sin(t) = √(1 - cos2(t))

This equation expresses sin(t) in terms of cos(t) and is valid when the terminal point determined by t is in quadrant II.