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**Unformatted text preview: **e < θ < π
2
(c) tan(θ) = 3
π
12
3π
16. If sin(α) = where 0 < α < and cos(β ) =
where
< β < 2π , ﬁnd the exact values
5
2
13
2
of the following.
(a) sin(α + β ) (b) cos(α − β ) (c) tan(α − β ) π
24
3π
5
where π < β <
, ﬁnd the exact values
17. If sec(α) = − where < α < π and tan(β ) =
3
2
7
2
of the following.
(a) csc(α − β ) (b) sec(α + β ) (c) cot(α + β ) 1
18. Let θ be a Quadrant III angle with cos(θ) = − . Show that this is not enough information to
5
θ
7π
3π
determine the sign of sin
by ﬁrst assuming 3π < θ <
and then assuming π < θ <
2
2
2
θ
and computing sin
in both cases.
2
√
√
√
2+ 3
6+ 2
19. Without using your calculator, show that
=
2
4
20. Drawing on part 4 of Example 10.4.3 for inspiration, write cos(4θ) as a polynomial in cosine.
Then write cos(5θ) as a polynomial in cosine. Can you ﬁnd a pattern so that cos(nθ) could
be written as a polynomial in cosine for any natural number n? 670 Fou...

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