The equation \( \csc(21^\circ) = \sec(\theta^\circ) \) can be solved by understanding the relationship between cosecant and secant. The cosecant function is the reciprocal of the sine function, and the secant function is the reciprocal of the cosine function. We need to find the angle \( \theta \) such that:

\[
\csc(21^\circ) = \sec(\theta^\circ)
\]

This implies that:

\[
\sin(21^\circ) = \cos(\theta^\circ)
\]

Using the identity \( \sin(\theta) = \cos(90^\circ - \theta) \), we can see that:

\[
\theta^\circ = 90^\circ - 21^\circ = 69^\circ
\]

Thus,

\[
\csc(21^\circ) = \sec(69^\circ)
\]

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. What is the general relationship between the secant and cosecant functions?
2. How do you convert between sine and cosine for complementary angles?
3. What is the value of \( \csc(21^\circ) \) approximately?
4. How does the identity \( \sin(\theta) = \cos(90^\circ - \theta) \) apply to other angles?
5. How can trigonometric identities simplify solving equations?

**Tip:** When dealing with complementary angles, remember that \( \sin(\theta) = \cos(90^\circ - \theta) \) and vice versa.

Discover how to solve the trigonometric equation csc(21°) = sec(69°) by using the relationship between sine and cosine for complementary angles. This solution breaks down the reciprocal function properties of sine and cosine, making it ideal for high school students in Grades 9-12.

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