Right Angle Trigonometry - April 21, 2014

Welcome back to Professor Baker's Math Class! On Monday, April 21st, we delved into the fascinating world of right angle trigonometry. Below, you'll find a recap of the key concepts we discussed, along with your assignments for Tuesday and Wednesday. Let's get started!

Class Notes: Trigonometric Ratios

Here's a summary of the trigonometric ratios we covered. Remember SOH CAH TOA!

  • Sine (sin): $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$
  • Cosine (cos): $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$
  • Tangent (tan): $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$
  • Cosecant (csc): $\csc(\theta) = \frac{\text{hypotenuse}}{\text{opposite}}$ (Reciprocal of sine)
  • Secant (sec): $\sec(\theta) = \frac{\text{hypotenuse}}{\text{adjacent}}$ (Reciprocal of cosine)
  • Cotangent (cot): $\cot(\theta) = \frac{\text{adjacent}}{\text{opposite}}$ (Reciprocal of tangent)

Where:

  • Opposite = Length of the side opposite to the angle $\theta$
  • Adjacent = Length of the side adjacent to the angle $\theta$
  • Hypotenuse = Length of the hypotenuse (the longest side)

Example:

Consider a right triangle with legs of length 3 and 4, and a hypotenuse of length 5. For angle $\theta$ opposite the side of length 4:

  • $\sin(\theta) = \frac{4}{5}$
  • $\cos(\theta) = \frac{3}{5}$
  • $\tan(\theta) = \frac{4}{3}$
  • $\csc(\theta) = \frac{5}{4}$
  • $\sec(\theta) = \frac{5}{3}$
  • $\cot(\theta) = \frac{3}{4}$

Special Right Triangles

We also briefly reviewed some special right triangles, including 30-60-90 and 45-45-90 triangles, and the associated trig ratios

Assignments for Tuesday and Wednesday:

  1. Khan Academy: Finish any assigned Khan Academy exercises on right angle trigonometry.
  2. Textbook Reading: Read Section 4.4 in your textbook.
  3. Practice Problems: Complete problems #3-90 every third problem in Section 4.4. This means doing problems 3, 6, 9, 12, and so on, up to 90.

Remember to show all your work and don't hesitate to ask questions if you're struggling! Good luck, and have a great week!