Sum Or Difference Of Two Angles Formula Sheet Page 4
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1
2
3
4
5
6Example (continued): Find the exact value of each expression.
tan40
tan10
c)
1 tan40 tan10
FINDING EXACT VALUES GIVEN THE VALUES OF SOME TRIGONOMETRIC FUNCTIONS
sin
cos
sin
tan
Example: Find the exact value of (a)
, (b)
, (c)
, (d)
given the following
5
4
cos
, 0 <
, sin
, -
0
information about and :
.
5
2
5
2
In order to use our sum and difference formulas, we need some more information. For parts (a), (b), and (c), we will
need to find sin() and cos() to plug into our formulas. For part (d) we will need tan() and tan() also.
5
The problem tells us that is in Quadrant ______. So draw a triangle in that quadrant that has an adjacent side of
and a hypotenuse of 5. Now use the Pythagorean Theorem to find the opposite side. Using this completed triangle, fill
in the following values: sin() = ___________ and tan() = _____________.
The problem also tells us that is in Quadrant ______. So draw a triangle in that quadrant that has an opposite side of 4
and a hypotenuse of 5. Now use the Pythagorean Theorem to find the adjacent side side. Using this completed triangle,
fill in the following values: cos() = ___________ and tan() = _____________.
Now we are ready to answer the questions that the original problem asked!
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