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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