Download Lesson 4-4: Sum and Difference Formulas for Sine and Tangent

Math 4 Honors
Lesson 4-4: Sum & Difference Formulas for Sine & Tangent
Name ___________________________
Date __________________________
Learning Goal:

Recall:
I can, without a calculator, use trigonometric identities such as angle addition/subtraction and
double angle formulas, to express values of trigonometric functions in terms of rational numbers and
radicals.
cos(   ) 
cos(   ) 
cos  cos   sin  sin 
But wait, there’s more…. The cosine sum formulas can be used to derive ones for sine.
sin(   ) 
sin(   ) 
sin  cos   cos  sin 
And the sine and cosine sum formulas can be used to derive ones for tangent.
tan(   )  tan   tan 
tan(  ) 
1  tan  tan 
  )Work
 only on the left side.
Verifytan(
this 
identity.
What do you think is the formula for
tan(  )?
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Page 2
Examples:
Find the exact values for the following.
1.
3.
5.
sin(310 ) cos(5 )  cos(310 )sin(5 ) 
 3 
 
tan 
  tan  
 16 
 16 
 3 
 
1  tan 
 tan  
 16 
 16 
Given:
Find:
2.
4.
3

cos   , 0   
5
2
1
3
sin    ,    
4
2
sin(   ) , cos(   ) ,
tan(   )
What quadrant is (α−β) in? How do you know?
 7 
tan 

 12 
sin 195

Math 4 Honors
Homework: Sum & Difference Formulas for Sine & Tangent
Name __________________________
Date _________________________
Simplify. Exact values only.
1.
tan  20   tan 10

1  tan  20  tan 10 
2.
sin(160 ) cos(50 )  cos(160 )sin(50 ) 
3. sin(80 ) cos(20 )  cos(80 )sin(20 ) 
4. tan(195°)
5. sin(105°)

6. sin 

 12 
17 
7. sin (α + β) – sin (α – β) =
8. sin (α + β) sin (α – β) =
Write in terms of sine only.
9. Rewrite sin 13x cos 2x – cos 13x sin 2x as an equivalent expression involving only the sine function.
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10. Given:
3
4
sin   , cos   ,  in quadrant II,  in quadrant IV
5
9
Find the following:
a. sin(  )
b. cos(  )
c. tan(  )
d. What quadrant is (  ) in?
Verify the following identities.


11. sin   x   cos x
2

12. sin    x   sin x