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 = 600

• 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(88.60)

• B) csc(5π/11)

• C) tan(7π/3)

• D) sec(1880)

• Assignment• Pg. 481• 7, 12, 15-37 odd