To calculate $\sin 120^\circ + \cos 90^\circ$, we evaluate each trigonometric function:

1. $\sin 120^\circ$: $\sin 120^\circ = \sin(180^\circ - 60^\circ) = \sin 60^\circ$ Using the exact value of $\sin 60^\circ$, we have: $\sin 120^\circ = \frac{\sqrt{3}}{2}$

2. $\cos 90^\circ$: The exact value of $\cos 90^\circ$ is: $\cos 90^\circ = 0$

Now, add the results: $\sin 120^\circ + \cos 90^\circ = \frac{\sqrt{3}}{2} + 0 = \frac{\sqrt{3}}{2}$

Final Answer:

$\sin 120^\circ + \cos 90^\circ = \frac{\sqrt{3}}{2}$

Would you like further details or have any questions?

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Related Questions:

1. How do you calculate trigonometric values for angles beyond $90^\circ$?
2. What is the unit circle and how does it help in finding trigonometric values?
3. What are the exact values of $\sin$ and $\cos$ for commonly used angles?
4. How does the sine function behave in different quadrants?
5. What is the relationship between $\sin$ and $\cos$ for complementary angles?

Tip:

Always remember that $\sin(180^\circ - x) = \sin x$ and $\cos(180^\circ - x) = -\cos x$ for angles in the second quadrant.