Math Analysis – Precalculus, Sullivan 10th Edition
Ch7Sec5Day3 1 3/3/2020
Section 7.5 – Trigonometric Equations – Day 3
Use Sum and Difference Formulas Involving Inverse Trigonometric Functions
Example 10: Find the exact value of :
11
13
cos sin cos
25
−−
+
You want the cosine of the sum of two angles,
11
sin 2
−
=
and
13
cos 5
−
=
.
Then
1
sin ,
2 2 2
−
=
and
3
cos , 0
5
=
.
Since
sin
is positive,
is in Quad I. Since
cos
is positive,
is in Quad I.
Use Pythagorean Identities to determine
cos
and
sin .
2
cos 1 sin=−
and
2
sin 1 cos=−
positive since each angle is in Quad I
2
1
12
=−
2
3
15
=−
1
14
=−
9
125
=−
3
4
=
16
25
=
3
2
=
4
5
=
So,
11
13
cos sin cos cos( )
25
−−
+ = +
cos cos sin sin =−
3 3 1 4
2 5 2 5
=−
3 3 4
10 10
=−
3 3 4
10
−
=
