10 - 2 Formulas for tan(a + b)


 
The sum and difference formulas for tangent are valid for values in which tan a, tan b, and tan(a +b) are defined.
Sum and Dfference formulas for Tangent
We can also use the tangent formula to find the angle between two lines.  We will get two cases which are supplementary to each other.  To find the angle in between two lines, we need to know the slope of both lines.  The equation looks like:



 sample problems

1)  Find the exact value of  tan 105o
Solution:

Use one of the above formulas.   Find a pair of numbers that you know the exact value of that add up to 105.  Try 45 and 60!! Use the addition formula!


2)  Find the two supplementary angles formed by the lines
y = 2x -5
and y = -3x + 2
Solution:
let m1 = 2 and m2 = -3

One angle is 45o and the other is 135o.



 
3)  If the tan x = -7/24 and cot y = 3/4, x is in quadrant II and y is in quadrant III, find each of the following:
        a)  tan(x + y)
        b)  tan(x - y)

Solution:

a)  Since the tangent and cotangent functions are reciprocals, tan y = 4/3

b)


4)  Verify tan(x - p/2) = -cot x

Solution:

Since the tangent is undefined at p /2, we must change to sine and cosine.



 
5)  Let sin x = 3/5 and sin y = 5/13 and both angles are in quadrant I, find tan(x + y).
Solution:
Since sin x = 3/5, cos x = 4/5 and tan x = 3/4.
Since sin y = 5/13, cos y = 12/13 and tan y = 5/12




 
Now let's take a look at the double and half-angle formulas!!