1. 6.1Right-Triangle Trigonometry Objectives: 1. Define the six trigonometric ratios of an acute angle in terms of a right triangle. 2. Evaluate trigonometric ratios, using triangles and on a calculator.

2. Units of Measure in a Circle Degrees: One degree is 1/360 th of a circle. Minutes: One minute is 1/60 th of a degree. Seconds: One second is 1/60 th of a minute or 1/3600 th of a degree. Degrees are not the smallest unit of measure in a circle. Sometimes measurements are written with Degree, Minutes, & Seconds (DMS Form).

3. Ex. #1Converting Between Decimal Form and DMS Form A. 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).

4. Ex. #1Converting Between Decimal Form and DMS Form B. 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.

5. Trigonometric Ratios Remember Soh – Cah – Toa

6. Memorizing the Reciprocal Functions 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

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

8. Ex. #3Evaluating Trig. Ratios on a Calculator 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.

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

10. Ex. #4Evaluating Trig. Ratios of Special Angles 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.

11. Ex. #4Evaluating Trig. Ratios of Special Angles 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.

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