5.3 & 5.4 Values of Trig Functions JB.notebook

5.3 & 5.4 Values of Trig Functions_JB.notebook1
May 1612:50 PM
5.3 & 5.4 1. Reference Angles (5.4) 2. Basic Graphs (5.3) 3. Periodic Functions (5.3) 4. Some More Identities (5.3) 5. Variations (5.3) 6. Equations and Inequalities
(5.3) 7. Inverse Functions (5.4)
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5.3 & 5.4 Values of Trig Functions_JB.notebook
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Reference angles allow us to ... • know some trig values outside of 0 < θ < π/2
• write equivalent statements that may be useful substitutions
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Find the exact values of sine, cosine, and tangent for the given angle.
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Find the exact values of sine, cosine, and tangent for the given angle.
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sin 75o =
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We can use reference angles to help us (finally) make the graphs of the
trigonometric functions.
Definition of a Periodic Function
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Warm-up: Complete Worksheet (Trig. Functions - Sine and Cosine)
Then answer the same questions about the other 4 trig functions.... i.e. y=tan(x) even, odd, or neither - explain
(tangent, cotangent, cosecant, secant)
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If a function is even then f(-x) = f(x)
Recall the definition of odd functions:
If a function is odd then f(-x) = -f(x)
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Knowing which trig functions are even or odd, Write a statement for each property you discovered.
for example: sin(x) is odd using what we know about odd functions, then
sin(-x) = -sin(x)
In your notes complete an equation for the other 5 trig functions.
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Refer to page 396....were the equations that you wrote correct?
You will use these for the next examples and then to verify.
Remember when you verify just work vertically using only one side and try to make it match the other side of the equal sign.
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5.35.4 Trig Functions
For homework you completed a chart for domain, range, asymptotes, xintercepts, etc.
Refer to pg 401 for a complete list of graph properties for the 6 trig functions...
Discuss as a group or in small groups the items written as a formula...do you understand each one?
Think about this as well:
Domain y = tan(x) could be written as
does it make sense?
can you explain it?
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Use reference angles and/or formulas for negatives to evaluate each expression.
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Use reference angles and/or formulas for negatives to evaluate each expression.
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See next worksheet titled "Graphing Trig Functions"
Once you are done making the graphs...you will use them to determine values
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y = sinθ
Use the approprite trig function graph to solve each equation or inequality on the interval x [2π, 2π]
draw the line y = 1/2....where does sin intersect the line?
sin(x) = 1/2 at 3300, 2100, 300, 3900
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how would the solutions have changed if there had not been a domain restriction in the previous cases?
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• if we do not need an exact value • if the angle is not special • if the angles reference angle is not special
We typically use the calculator.
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If θ is an acute angle and sin θ = 0.6635, approximate θ.
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Why did it need to be stated that θ was an acute angle in the last problem?
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HOLD IT!
Trig functions are not 1to1! How can they have inverses?!?!?
Inverses
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So, the solutions you get out of the inverse trig functions on your calculator may or may not be the solution you want.
to do these types of problems.....I think,
What is my reference angle?
what quadrant am I in?
what sign is this trig function?
Your calculator may not have the correct SIGN you want
See page 412 to see what domain restrictions your calculator assumes
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If tan θ = 0.4623 for 0o < θ < 360o, approximate θ to the nearest 1o.
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If cos θ = 0.3842 for 0 < θ < 2π, approximate θ to the nearest 0.0001 radian.
Apr 304:27 PM
Monday we will review 5.3-5.3
take any questions from Thur/Fri
and Review for quiz 5.3-5.4
we will need to probably refresh on reference angles...so please review your notes.
PS since I'm not here....your graphs quiz is on Monday :)
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By the end of this section you should know:
· know how values of a trig function vary as the input varies
· definition of a periodic function
· graphs of sine and cosine functions
· formulas for negatives
· the definition of a reference angle
· understand the relationship between the trigonometric functions and their inverses
· understand the limitations of the inverse trigonometric function buttons on the calculator
By the end of this section you should be able to:
· create the graphs of sine and cosine
· use the graphs of trigonometric functions to solve equations and inequalities
· complete statements of variation for the trigonometric functions
· sketch the graphs of trigonometric functions involving transformations
· solve applied problems involving trigonometric functions
· calculate the reference angle for a given angle
· sketch a reference angle on a coordinate plane
· use reference angles to evaluate trigonometric functions of a given angle
· evaluate trigonometric functions on a calculator
· use inverse trigonometric functions to calculate an angle given the value of the trigonometric function
· use reference angles to get the correct value if outside of the limits of the calculator
· solve applied problems involving reference angles
· solve applied problems involving inverse trigonometric functions
SMART Notebook
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5.3 & 5.4 Values of Trig Functions JB.notebook