We are given that $\sin \theta = a$ and that $\theta$ is an angle in the first quadrant. We are asked to evaluate $\cos(270^\circ - \theta)$ in terms of $a$.

Step-by-step solution:

1. Using the cosine identity: We can use the identity: $\cos(270^\circ - \theta) = -\sin(\theta)$

   This identity comes from the fact that subtracting an angle from $270^\circ$ shifts the reference angle into the third quadrant, where cosine is negative, and the sine of the angle is equivalent to the cosine of its complement.

2. Substitute $\sin \theta = a$: Since we are given that $\sin \theta = a$, we substitute this into the expression: $\cos(270^\circ - \theta) = -a$

Thus, the value of $\cos(270^\circ - \theta)$ in terms of $a$ is $-a$.

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Would you like further clarification or a deeper explanation?

Here are five related questions to expand your understanding:

1. How does the unit circle help in understanding angle transformations?
2. What are the other trigonometric identities for angles involving $270^\circ$?
3. How can you express $\sin(270^\circ - \theta)$ in terms of $a$?
4. What happens to the trigonometric ratios of angles in the different quadrants?
5. Can we generalize the result for any angle of the form $360^\circ - \theta$?

Tip: Remember that angles subtracted from $270^\circ$ or $90^\circ$ often involve using sine and cosine in complementary ways.