Math 1316
Fundamental Identities
Section 5.1 Class Notes
An even function is symmetrical with respect to the y-axis.
f (  x)  f ( x )
The cosine function is even:
y
-2
-

cos( x)  cos( x)
1
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2
x
Math 1316
Section 5.1 Class Notes
An odd function is symmetrical with respect to the origin.
f ( x )   f ( x )
The sine function is odd:
y
x
-2
-

2
sin(  x)   sin( x)
2
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Math 1316
Section 5.1 Class Notes
Finding Trigonometric Function Values given one Value and the Quadrant.
Example:
Find the remaining five trigonometric functions of θ.
25.
sin θ = 2/3, θ in quadrant II.
3
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Math 1316
27.
Section 5.1 Class Notes
tan θ = -1/4 , θ in quadrant IV.
4
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Math 1316
31. sec θ = 4/3 , sin θ < 0.
Section 5.1 Class Notes
5
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Math 1316
Example:
Section 5.1 Class Notes
For each expression in Column I, choose the expression from Column II that completes an identity.
6
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Math 1316
Section 5.1 Class Notes
7
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Math 1316
Expressing one function in terms of another.
Section 5.1 Class Notes
Example: Write the first trigonometric function in term of the second trigonometric function.
47. sinx , cos x.
52. sec x ,
sinx.
Rewrite an expression in terms of sine and cosine.
Example: Simplify each expression so that no quotients appear in the final expression.
53. cot θ sin θ
8
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Math 1316
Section 5.1 Class Notes
59 . (1 – cos θ)(1 + sec θ)
61.
cos2   sin 2 
sin  cos 
65. sin  (csc   sin  )
9
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Math 1316
66.
Section 5.1 Class Notes
1  tan 2 x
1  cot 2 x
10
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