1. Right Triangle Trigonometry
Algebra 2 with Trigonometry
Ms. Lee

2. 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

3. 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

4. Right Triangle Trigonometry𝜽 A H O
hypotenuse
opposite A H O
adjacent A

5. 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)

6. 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)

7. 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

8. 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