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Presentation transcript:

Copyright © 2014 Pearson Education, Inc. 10 CHAPTER 10.1 Sine and Cosine Ratios Copyright © 2014 Pearson Education, Inc.

Copyright © 2014 Pearson Education, Inc. Trigonometric Ratios The word trigonometry is derived from ancient Greek and means “three-angle measurement” or “triangle measurement.” Recall that any two similar right triangles have equal angle measures and the ratios of their corresponding sides are equivalent. Because these similar right triangles have equal ratios, we call these ratios trigonometric ratios and we give them special names, as we see next. Copyright © 2014 Pearson Education, Inc.

Copyright © 2014 Pearson Education, Inc. Trigonometric Ratios Copyright © 2014 Pearson Education, Inc.

Writing Trigonometric Ratios What are the sine, and cosine∠T? Solution The opposite value and the adjacent value depend on the angle. We are interested in ∠T, so opposite ∠T is 8 units and the leg adjacent to ∠T is 15 units. Copyright © 2014 Pearson Education, Inc.

Writing Trigonometric Ratios for 45° Find the sine, and the cosine of 45°. Give an exact value and a four-decimal place approximation. Solution Since the legs are the same length, choose one of the two 45° angles. Copyright © 2014 Pearson Education, Inc.

Writing Trigonometric Ratios for 45° Copyright © 2014 Pearson Education, Inc.