Write the first expression in terms of the second if the terminal point determined by t is in the given quadrant.
sin(t), cos(t);
 Quadrant II
sin(t) =

In Quadrant II, sine is positive and cosine is negative. We can relate sine and cosine using the Pythagorean identity:

\[
\sin^2(t) + \cos^2(t) = 1
\]

Solving for \(\sin(t)\):

\[
\sin(t) = \sqrt{1 - \cos^2(t)}
\]

Since \( \sin(t) \) is positive in Quadrant II, the expression for \( \sin(t) \) in terms of \( \cos(t) \) is:

\[
\sin(t) = \sqrt{1 - \cos^2(t)}
\]

Would you like more details or have any questions?

Here are 5 related questions for practice:
1. What is the expression for \(\cos(t)\) in terms of \(\sin(t)\) in Quadrant II?
2. How does the Pythagorean identity relate sine and cosine?
3. What is the value of \(\tan(t)\) in terms of \(\sin(t)\) and \(\cos(t)\)?
4. What changes for sine and cosine in Quadrant III?
5. How do the signs of trigonometric functions vary across all four quadrants?

**Tip**: Always consider the signs of trigonometric functions in each quadrant.

Write the first expression in terms of the second if the terminal point determined by t is in the given quadrant. sin(t), cos(t); Quadrant II sin(t) =

Learn how to express sine in terms of cosine when the terminal point is in Quadrant II. This trigonometry problem explores the Pythagorean identity and the behavior of sine and cosine in different quadrants. Ideal for students in Grades 10-12.

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