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Right Triangle Trigonometry Algebra 2 with Trigonometry Ms. Lee Essential Stuff: Essential Questions: • How do you find lengths of sides in a right triangle? • How do you find the measure of a missing angle in a right triangle? Essential Vocabulary: right triangle, sine, cosine, tangent Pythagorean Theorem • Can only be used for right triangles • Given the measure of any two sides of a right triangle, the Pythagorean theorem can be used to find the measure of the remaining side. • Pythagorean Theorem: 𝑎2 +𝑏 2 = 𝑐 2 • C must be the hypotenuse Right Triangle Trigonometry O opposite sin H hypotenuse A adjacent cos hypotenuse H O opposite tan adjacent A 𝜽 A adjacent O opposite hypotenuse H Reciprocal Trigonometric Ratios • There are three additional trigonometric ratios called the reciprocal ratios. 1. 𝑐𝑠𝑐𝜃 = ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 (reciprocal of sine) 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 2. 𝑠𝑒𝑐𝜃 = ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 3. 𝑐𝑜𝑡𝜃 = 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 (reciprocal of tangent) 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 (reciprocal of cosine) Reciprocal Trigonometric Ratios • There are three additional trigonometric ratios called the reciprocal ratios. 1. 2. 3. 1 𝑐𝑜𝑠𝑒𝑐𝑎𝑛𝑡𝜃 (𝑐𝑠𝑐𝜃) = (reciprocal of sine) 𝑠𝑖𝑛𝜃 1 𝑠𝑒𝑐𝑎𝑛𝑡𝜃 (𝑠𝑒𝑐𝜃) = (reciprocal of cosine) 𝑐𝑜𝑠𝜃 1 𝑐𝑜𝑡𝑎𝑛𝑔𝑒𝑛𝑡𝜃 (𝑐𝑜𝑡𝜃) = (reciprocal of tangent) 𝑡𝑎𝑛𝜃 Using the Ratios • You can use the ratios discussed in the previous slides along with the Pythagorean Theorem to find missing sides and angles in a right triangle. • When using your calculator: • To find a side use sin, cos, and tan keys • To find an angle use inverses (2nd sin, 2nd cos, 2nd tan) • Make sure your calculator is in degree mode. • Examples Quiz 1 Tomorrow: • List the 6 Trigonometric Ratios • State the Pythagorean Theorem • Give the 3 Reciprocal Functions Homework 9.1