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: 𝑎 2 + 𝑏 2 = 𝑐 2 C must be the hypotenuse

Right Triangle Trigonometry 𝜽 A H O hypotenuse opposite A H O adjacent A

Reciprocal Trigonometric Ratios There are three additional trigonometric ratios called the reciprocal ratios. 𝑐𝑠𝑐𝜃= ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 (reciprocal of sine) 𝑠𝑒𝑐𝜃= ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 (reciprocal of cosine) 𝑐𝑜𝑡𝜃= 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 (reciprocal of tangent)

Reciprocal Trigonometric Ratios There are three additional trigonometric ratios called the reciprocal ratios. 𝑐𝑜𝑠𝑒𝑐𝑎𝑛𝑡𝜃 (𝑐𝑠𝑐𝜃)= 1 𝑠𝑖𝑛𝜃 (reciprocal of sine) 𝑠𝑒𝑐𝑎𝑛𝑡𝜃 (𝑠𝑒𝑐𝜃)= 1 𝑐𝑜𝑠𝜃 (reciprocal of cosine) 𝑐𝑜𝑡𝑎𝑛𝑔𝑒𝑛𝑡𝜃 (𝑐𝑜𝑡𝜃)= 1 𝑡𝑎𝑛𝜃 (reciprocal of tangent)

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

List the 6 Trigonometric Ratios State the Pythagorean Theorem Quiz 1 Tomorrow: List the 6 Trigonometric Ratios State the Pythagorean Theorem Give the 3 Reciprocal Functions Homework 9.1