6.2.1 – The Basic Trig Functions

Now, we have a few ways to measure/view angles – Degrees – Radians – Unit Circle – Triangles

3 Basic Functions Say we have a right triangle similar to the example below, with the angle ϴ We can define the following as: Sin(ϴ) = Opp/Hyp Cos(ϴ) = Adj/Hyp Tan(ϴ) = Sin/Cos OR Opp/Adj ϴ = Radians

Example. Find the following trig functions given the triangle below: Sin(ϴ) = Cos(ϴ) = Tan(ϴ) =

Example. Find the following trig functions given the triangle below. Let ϴ = 60 0 Sin(ϴ) = Cos(ϴ) = Tan(ϴ) =

The other 3 trig functions We can define 3 more basic trig functions Call them the “reciprocal” functions csc(ϴ) = 1/sin(ϴ) = hyp/opp sec(ϴ) = 1/cos(ϴ) = hyp/adj cot(ϴ) = 1/tan(ϴ) = adj/opp

Example. Find the following trig functions given the triangle below: csc(ϴ) = sec(ϴ) = cot(ϴ) =

Example. Evaluate the tangent and secant from the following triangle if ϴ = π/6. What do we know about the angle measure of π/6?

Using Your Calculator We may evaluate any of the 6 basic trig functions for ANY angle Just a small issue… – Radians? – Degrees? Which one do we all prefer? Regardless, at some point we all have to convert

Example. Evaluate the following using your calculator. A) sin( ) B) csc(5π/11) C) tan(7π/3) D) sec(188 0 )

Assignment Pg , 12, odd