1 / 12

Understanding Right Triangle Trigonometry: Ratios, Conversions, and Evaluations

This guide introduces the six trigonometric ratios for acute angles using right triangles, including sine, cosine, tangent, and their reciprocals. It explains how to evaluate these ratios using triangles and calculators, ensuring the calculator is set to Degree mode. You'll also learn about converting degrees to minutes and seconds (DMS) and vice versa. Additionally, special angles such as 30°, 45°, and 60° are explored for practical application of trigonometric ratios. Master these essential trigonometric concepts for effective mathematical problem-solving.

abdalla
Télécharger la présentation

Understanding Right Triangle Trigonometry: Ratios, Conversions, and Evaluations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 6.1 Right-Triangle Trigonometry Objectives: Define the six trigonometric ratios of an acute angle in terms of a right triangle. Evaluate trigonometric ratios, using triangles and on a calculator.

  2. Degrees are not the smallest unit of measure in a circle. Sometimes measurements are written with Degree, Minutes, & Seconds (DMS Form). Units of Measure in a Circle

  3. Write in decimal form: Since there are 60 seconds in a minute, the 9” needs divided by 60 twice, or just divided by 3600 which is 60(60). Ex. #1 Converting Between Decimal Form and DMS Form

  4. Write in DMS form: Truncate the decimal by removing whole units and multiply the remainder by seconds. Repeat the process a second time and you have DMS Form. Ex. #1 Converting Between Decimal Form and DMS Form

  5. Remember Soh – Cah – Toa Trigonometric Ratios

  6. The reciprocal functions can be memorized by remembering that the prefix of “co-” is used only once in each pair. Start with the easiest pair to remember: • tangent / cotangent • sine / cosecant • cosine / secant Memorizing the Reciprocal Functions

  7. Evaluate the six trigonometric ratios of the angle θ, as shown below: Ex. #2 Evaluating Trigonometric Ratios

  8. Evaluate the six trigonometric ratios of 15° using a calculator. NOTE: Make sure your calculator is set to Degree Mode first! The 3 main functions are easy to enter, but to do the reciprocal functions we must do what their name says, take the reciprocal. Ex. #3 Evaluating Trig. Ratios on a Calculator

  9. Evaluate the six trigonometric ratios of 30°, 60°, & 45° on the triangles below: Ex. #4 Evaluating Trig. Ratios of Special Angles

  10. Evaluate the six trigonometric ratios of 30°, 60°, & 45° on the triangles below: Finding the reciprocal functions on this is fairly easy. Some values may still need rationalized. Ex. #4 Evaluating Trig. Ratios of Special Angles

  11. Evaluate the six trigonometric ratios of 30°, 60°, & 45° on the triangles below: For 60° the values for sine and cosine switch places as well as the values for tangent and cotangent. Ex. #4 Evaluating Trig. Ratios of Special Angles

  12. Evaluate the six trigonometric ratios of 30°, 60°, & 45° on the triangles below: For 45° sine and cosine have the same values. Ex. #4 Evaluating Trig. Ratios of Special Angles

More Related