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Math Topics

Trigonometry

The Six Trigonometric Functions

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Angles, Degrees, and Special Triangles

A ladder is leaning against a wall. The top of the ladder is \(4\) feet above the ground and the bottom of the ladder makes an angle of \(60^{\circ}\) with the ground. How long is the ladder, and how far from the wall is the bottom of the ladder?

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The Rectangular Coordinate System

Suppose a Ferris wheel has a radius of 50 feet, with the bottom of the wheel 10 feet above the ground. Let t represent the time (in minutes). If the wheel completes one revolution in 2 minutes, find the distance a rider is above the ground when the ride starts (t = 0), after 30 seconds (t = Ã¢â‚¬Â¯1/Ã¢â‚¬Â¯2Ã¢â‚¬Â¯), at one minute (t = 1), 30 seconds later (t = Ã¢â‚¬Â¯3Ã¢â‚¬Â¯/Ã¢â‚¬Â¯2Ã¢â‚¬Â¯), and at 2 minutes (t = 2).

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Definition I: Trigonometric Functions

Suppose a Ferris wheel has a radius of 50 feet, with the bottom of the wheel 10 feet above the ground. If the wheel completes one revolution in 2 minutes, find the distance a rider is above the ground when the rider is at point A on the wheel.

**Mini Lecture**

Find the six trigonometric functions of \(\theta\) if \((-5,12)\) is on the terminal side.

Find sine, cosine, and tangent of \(-45^{\circ}\).

If \(\tan{\theta}=\displaystyle\frac{3}{4}\) and \(\theta\in\) QI, find \(\sin{\theta}\) and \(\cos{\theta}\).

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Introduction to Identities

**Mini Lecture**

If \(\sin{\theta}=\frac{4}{5}\) and \(\csc{\theta}\).

Find \(\cot{\theta}\) if \(\sin{\theta}=-\frac{5}{13}\) and \(\cos{\theta}=-\frac{12}{13}\).

Find \(\cos{\theta}\) if \(\sin{\theta}=\frac{1}{3}\) and \(\theta\in\) QII

\(\cos{\theta}=\frac{12}{13}\) with \(\theta\in\) QI, then find \(\sin{\theta}\), \(\sec\theta\), \(\tan\theta\), \(\cot\theta\), and \(\csc\theta\).

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More on Identities

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Spotlight on Julieta

**Spotlight on Julieta**

Julieta speaks about her experience with A.V.I.D.

Achievement Via Individual Determination is a non-profit organization that provides professional learning for educators to improve college readiness for all students, especially those traditionally underrepresented in higher education.