Download 15.4 Sine and Tangent of a Sum or Difference

15.4 Sine and Tangent of a Sum
or Difference
Sine of a Sum or Difference Identity
sin      sin  cos   cos  sin 
Tangent of a Sum or Difference Identity
tan   tan 
tan     
1 tan  tan 
Express each of the following as a
single sine or tangent and evaluate.
1.
sin 335 cos110  cos 335 sin110
o
o
o
o
Express each of the following as a
single sine or tangent and evaluate.
tan155  tan 20
o
o
1  tan155 tan 20
o
2.
o
• To use the sum or difference identity to find the
value of a trig function, first make sure the angle
is in degrees – it is much easier to work with.
• Then, you want to find two “nice” numbers that
add/subtract to the angle measure. There is
more than one answer!
• Hint: If your angle ends in a 5, then 45 will be
one of the angles.
• Then, use the sum or difference identity to find
the value of sine or tangent.
Use the formulas for the sine and
tangent of a sum and difference, then
evaluate.
3.
sin105
o
Use the formulas for the sine and
tangent of a sum and difference, then
evaluate.
4.

tan 15
o

Use the formulas for the sine and
tangent of a sum and difference, then
evaluate.
5.
11
sin
12
Use the formulas for the sine and
tangent of a sum and difference, then
evaluate.
6.
17
tan
12
7. Find the exact value of each trigonometric function
given:
15 
cos x   ;  x  
17 2
a.
sin x  y 
b.
sin x  y 
4 3
sin y   ;
 y  2
5 2
8. Find the exact value of each trigonometric function
given:
24

sin x  ; 0  x 
25
2
a.
sin x  y 
b.
sin x  y 
4

cos y  ; 0  y 
5
2