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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
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