# Applying inverse trig function with model | Trigonometry | Khan Academy | Summary and Q&A

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February 3, 2014
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Applying inverse trig function with model | Trigonometry | Khan Academy

## TL;DR

Determine the number of days after January 7th that the temperature in Santiago, Chile reaches 20 degrees Celsius in the spring.

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### Q: Why is it important to consider the concept of seasons in the southern hemisphere?

Understanding the seasons is crucial to determining the first day of spring and accurately predicting when the temperature will reach 20 degrees Celsius. It helps identify the correct point in the year to focus on in the mathematical equation.

### Q: How does the mathematical equation help calculate the number of days for the first spring day?

The equation, 20 = 7.5cos(2π/365)t + 21.5, relates the temperature in Santiago, Chile to the number of days after January 7th. By rearranging the equation and solving for cosine, the value of D can be determined to find the number of days.

### Q: Why is it necessary to be cautious while applying the inverse cosine function?

The inverse cosine function provides multiple angles that correspond to the same cosine value. In this case, there are two angles that result in cosine equal to -0.2. Considering the correct angle is crucial to finding the first spring day instead of the fall day.

### Q: How is the correct angle determined when applying the inverse cosine function?

By drawing a unit circle and noting the different seasons and angles, the correct angle for the first spring day can be identified. Subtracting the obtained angle from 2π or adding 2π if needed ensures the desired angle within the spring season.

## Summary & Key Takeaways

• The video discusses how to calculate the number of days after January 7th when the temperature in Santiago, Chile reaches 20 degrees Celsius in the spring.

• The concept of seasons in the southern hemisphere is explained, with a focus on identifying the first day of spring.

• A mathematical equation is used to model the temperature in Santiago, Chile, and solve for the number of days to reach 20 degrees Celsius in the spring.