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The document you uploaded contains a **math improvement plan for trimester II** from **Colegio Ofelia Uribe de Acosta I.E.D.** The topics evaluated include:

1. Right triangles (Pythagoras theorem)
2. Introduction to trigonometric ratios in right triangles
3. Trigonometric functions
4. Graphs of trigonometric functions

The exercises provided in the plan include:

1. A problem about solving the sides of a triangle PQR where \( r = 2q \) and asking for the measure of side \( p \).
2. A problem involving the Tower of Pisa, including determining the other angle given a tilt of 4°, calculating the percentage of visitors without reservations, and estimating weekly revenues based on provided data.
3. A problem related to a technical drawing triangle (right triangle), where the hypotenuse is twice the length of the shorter leg, and the longer leg is 32 cm.
4. A problem about a ladder placed on a wall, asking to calculate the cosine of the angle between the ground and the ladder.
5. An analysis of the sine function graph between \( 0 \) and \( 2\pi \), including questions about its period, domain, range, and intervals where the function is increasing or decreasing.
6. A question about determining the height of a projectile using appropriate functions in the absence of air resistance.
7. A graph-based question requiring determining the period, domain, the function's value at \( x = 1 \), and its range.

Would you like help with any specific exercise or concept from this plan?

Here are 5 follow-up questions to expand on the material:

1. How is the Pythagorean theorem applied to find the unknown side of a right triangle?
2. What are the basic trigonometric ratios, and how do they relate to right triangles?
3. How do you determine the period of a sine function from its graph?
4. What is the relationship between a triangle's angles and its sides in terms of trigonometric functions?
5. What are common real-life applications of trigonometric functions?

**Tip**: Always verify that the triangle you're analyzing is a right triangle before applying trigonometric ratios.

The document you uploaded contains a math improvement plan from Colegio Ofelia Uribe de Acosta I.E.D. for trimester II, with exercises focusing on topics like right triangles, trigonometric ratios, and graphing trigonometric functions. Examples include calculating the side of a triangle, determining angles, calculating percentages, and graph analysis.

This improvement plan focuses on key mathematical concepts like right triangles, the Pythagoras theorem, and trigonometric ratios. Problems include calculating triangle sides, angle determination, and graphing sine functions. Ideal for students in Grades 9-11.

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