We will evaluate the trigonometric values for each angle:

1. \(\sin 30^\circ = \frac{1}{2}\)
2. \(\cos 45^\circ = \frac{\sqrt{2}}{2}\)

Now, add these two values:

\[
\sin 30^\circ + \cos 45^\circ = \frac{1}{2} + \frac{\sqrt{2}}{2}
\]

Since the denominators are the same, you can combine the numerators:

\[
= \frac{1 + \sqrt{2}}{2}
\]

Thus, the final answer is:

\[
\boxed{\frac{1 + \sqrt{2}}{2}}
\]

Would you like a more detailed breakdown of how I arrived at this? 

Here are some related questions:
1. What is \(\cos 30^\circ + \sin 45^\circ\)?
2. How do you simplify \(\sin 60^\circ + \cos 30^\circ\)?
3. What is the exact value of \(\sin 45^\circ + \cos 60^\circ\)?
4. How do trigonometric values of standard angles relate to the unit circle?
5. Can you derive trigonometric values using right triangles?

**Tip:** Knowing standard trigonometric values (e.g., 30°, 45°, 60°) helps solve many problems quickly.

Learn how to evaluate the sum of sin 30° and cos 45° using standard trigonometric values. This step-by-step solution explains the process and provides insight into core trigonometric concepts, ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation