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**Unformatted text preview: **s long as we use − , 0 ∪ 0,
as the range
2
2 of f (x) = arcsec(x).
13. Show that arccsc(x) = arcsin
of f (x) = arccsc(x).
14. Show that arcsin(x) + arccos(x) =
15. If sin(θ) = π
for −1 ≤ x ≤ 1.
2 x
π
π
for − < θ < , ﬁnd an expression for θ + sin(2θ) in terms of x.
2
2
2 10.6 The Inverse Trigonometric Functions 723 x
π
π
1
1
for − < θ < , ﬁnd an expression for θ − sin(2θ) in terms of x.
7
2
2
2
2
x
π
17. If sec(θ) = for 0 < θ < , ﬁnd an expression for 4 tan(θ) − 4θ in terms of x.
4
2 16. If tan(θ) = 18. Solve the following equations using the techniques discussed in Example 10.6.7 then approximate the solutions which lie in the interval [0, 2π ) to four decimal places.
7
11
2
cos(x) = −
9
sin(x) = −0.569
cos(x) = 0.117
sin(x) = 0.008
359
cos(x) =
360
tan(x) = 117
cot(x) = −12 3
2 (a) sin(x) = (i) sec(x) = (b) 90
17
√
(k) tan(x) = − 10 (c)
(d)
(e)
(f)
(g)
(h) (j) csc(x) = − (l) sin(x) = 3
8 7
16
(n) tan(x) = 0.03 (m) cos(x) = − 19. Find the two acute angles in the right triangle whose sides ha...

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