Agenda EQ: What are the 6 trig functions? Turn in Portfolio Warm Up Notes on 6 trig functions Practice Study Guide for Midterm Homework: 3A—don’t take up homework if most did not do it.

Warm Up What is the Pythagorean Theorem (formula)? 2. 3. 4. Solve for the missing side of each of the following triangles: 2. 3. 4.

Trigonometric Ratios A RATIO is a comparison of two numbers. For example: boys to girls cats : dogs right : wrong In Trigonometry, the comparison is between sides of a triangle.

We need to do some housekeeping before we can proceed…

θ this is the symbol for an unknown angle measure. It’s name is ‘Theta’. Don’t let it scare you… it’s like ‘x’ except for angle measure… it’s a way for us to keep our variables understandable and organized.

The Trigonometric Ratios only work for RIGHT TRIANGLES!! The only angles we use are the 2 acute angles.

We use lowercase letters to represent the sides of a triangle. We use uppercase letters or greek letters to represent the angles of a triangle.

Here we go!!!!

SOH CAH TOA O S H A C H O T A One more time… Here are the ratios: sinθ = opposite side hypotenuse H A C cosθ = adjacent side hypotenuse H O T tanθ =opposite side adjacent side A SOH CAH TOA

Ratio of an angle measure Trigonometric Ratios Name “say” Sine Cosine Tangent Cosecant Secant Cotangent Abbreviation Abbrev. sin cos tan csc sec cot Ratio of an angle measure sin𝜃 = 𝑂 𝐻 c𝑜𝑠𝜃 = 𝐴 𝐻 t𝑎𝑛𝜃 = 𝑂 𝐴 c𝑠𝑐𝜃 = 𝐻 𝑂 s𝑒𝑐𝜃 = 𝐻 𝐴 c𝑜𝑡𝜃 = 𝐴 𝑂

Let’s practice… B c a C b A Write the ratio for sin A Sin A = Write the ratio for cos A Cos A = Write the ratio for tan A Tan A = B c a C b A Let’s switch angles: Find the sin, cos and tan for Angle B: Tan B = Sin B = Cos B =

More Practice… C 2cm B A 3cm Find an angle that has a tangent (ratio) of 2 3 C 2cm B A 3cm

Even More Practice… For the given triangle find: sin 𝜃 = sin 𝛽 = cos 𝜃 = cos 𝛽 = tan 𝜃= tan 𝛽=

Evaluate the following: sin 45 = cos 56 = tan 25 =