6.1
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Trigonometry
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Trigonometry
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Lesson 3 Precalculus Online
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Lesson 3: Trigonometric Functions Topic 3: Reference Angles Examples : Find the reference angle for each angle. 1. Find the reference angle for 218?. Find the positive acute angle made by the terminal side of the angle and the x-axis: The reference angle for 218? is 218? - 180? = 38? 2. Find the reference angle for 1387 ? First find a coterminal angle between 0? and 360?. Divide 1387 by 360 to get a quotient of about 3.9. So subtract 360 three times. 1387? ? 3(360? ) = 307?. The reference angle for 307 ? is 360? ? 307? = 53? 360? ? 307? = 53? 3. Find the reference angle for -237? Find a coterminal positive angle by adding 360?: -237? + 360? = 123? The reference angle for 123? is 180? - 123? = 57?. 180 ? ? 123 ? = 57 ? 180? ? 123? = 57? Practice
Trig functions
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Review : Trig Functions The intent of this section is to remind you of some of the more important (from a Calculus standpoint?) topics from a trig class. One of the most important (but not the first) of these topics will be how to use the unit circle. We will actually leave the most important topic to the next section. First let?s start with the six trig functions and how they relate to each other. Recall as well that all the trig functions can be defined in terms of a right triangle. From this right triangle we get the following definitions of the six trig functions. Remembering both the relationship between all six of the trig functions and their right triangle definitions will be useful in this course on occasion.
Trig cheat sheet
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? 2005 Paul Dawkins Trig Cheat Sheet Definition of the Trig Functions Right triangle definition For this definition we assume that 0 2 pq< < or 0 90q? < < ? . oppositesin hypotenuseq = hypotenusecsc oppositeq = adjacentcos hypotenuseq = hypotenusesec adjacentq = oppositetan adjacentq = adjacentcot oppositeq = Unit circle definition For this definition q is any angle. sin 1 y yq = = 1csc yq = cos 1 x xq = = 1sec xq = tan yxq = cot x yq = Facts and Properties Domain The domain is all the values of q that can be plugged into the function. sinq , q can be any angle cosq , q can be any angle tanq , 1 , 0, 1, 2,2n nq p ? ?? + = ? ?? ?? ? K
Trigonometric Ratios
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Trig Ratios:
sin y/r
cos x/r
tan y/x
cot x/y
sec r/x
csc r/y
Trig. Function Derivatives: sine, cosine, and tangent.
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The derivatives of the basic trig. functions are as follows:
f(x)=sin(x) / f`(x)=cos(x)
f(x)=cos(x) / f`(x)=-sin(x)
f(x)=tan(x) / f`(x)=sec^2(x)
Pythagorean theory
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a squared plus b squared equals c squared, this is use to find missing sides of a triangle c= hypotenuse or the longest leg
Trig Functions Chapter 1.2
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Copyright ? 2009 Pearson Addison-Wesley 1.2-* 1 Trigonometric Functions Copyright ? 2009 Pearson Addison-Wesley Copyright ? 2009 Pearson Addison-Wesley 1.2-* 1.1 Angles 1.2 Angle Relationships and Similar Triangles 1.3 Trigonometric Functions 1.4 Using the Definitions of the Trigonometric Functions 1 Trigonometric Functions Copyright ? 2009 Pearson Addison-Wesley Copyright ? 2009 Pearson Addison-Wesley 1.1-* 1.2-* Angle Relationships and Similar Triangles 1.2 Geometric Properties ? Triangles Copyright ? 2009 Pearson Addison-Wesley 1.1-* Copyright ? 2009 Pearson Addison-Wesley 1.1-* 1.2-* Vertical Angles The pair of angles NMP and RMQ are vertical angles. Vertical angles have equal measures. Copyright ? 2009 Pearson Addison-Wesley 1.1-*
Easy way to remember the positives and negatives of the trigonometric functions on a graph
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All you have to remember is " All Students Take Calculus"
Stating from the first quad, its A for I, S for II, T for III, and C for IV.
the acronyms stand for which of the functions are positive.
A stands for all, all the functions are positive
S stands for Sin, Only sin and csc are positive, rest are negative
T stands for Tan, Only tan and cot are positive, rest are negative
C stands for Cos, Only cos and sec are positive, rest are negative
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