1. θ
hypotenuse
adjacent
opposite θ
hypotenuse
opposite
adjacent
The opposite and adjacent sides change depending on which acute angle you use.
There are 6 trig ratios that can be formed from the acute angle θ.
Sine θ = sin θ Cosecant θ = csc θ
Cosine θ = cos θ Secant θ = sec θ
Tangent θ = tan θ Cotangent θ = cot θ

2. If we know 2 sides of a right triangle how can we find the third side?
Pythagorean theorem: leg2 + leg2 = hypotnuse2
Example: 6
h2 = l = 112
h2 = l = 121
h2 = l2 = 57
h = √ l = √57
h = 2√13

3. Lets combine the two slides
If we know all 3 sides of a right triangle we can find the ratio that each trig function.
Lets take the first example:
2√13
ø from whichever angle is marked we can state the
6 trig ratios.
Sin ø = 4/2√13 = 2/√13
Cos ø = 6/2√13 = 3/√13
Tan ø = 4/6 = 2/3
Csc ø = 2√13/4 = √13/2
Sec ø = 2√13/6 = √13/3
Cot ø = 6/4 = 3/2

4. Homework assignment # 1 Pg. 516 (9-18 all)