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6.1 Right-Triangle Trigonometry

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.

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6.1 Right-Triangle Trigonometry

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  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

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