Unformatted text preview: l) y = 1
cot 2x +
2 +1 3. Using Example 10.5.3 as a guide, show that the following functions are sinusoids by rewriting
them in the forms C (x) = A cos(ωx + φ) + B and S (x) = A sin(ωx + φ) + B for ω > 0.
(a) f (x) = 2 sin(x) + 2 cos(x) + 1
(c) f (x) = − sin(x) + cos(x) − 2
(d) f (x) = − sin(2x) −
(b) f (x) = 3 3 sin(3x) − 3 cos(3x)
4. Let φ be an angle measured in radians and let P (a, b) be a point on the terminal side of φ
when it is drawn in standard position. Use Theorem 10.3 and the sum identity for sine in
Theorem 10.15 to show that f (x) = a sin(ωx) + b cos(ωx) + B (with ω > 0) can be rewritten
as f (x) = a2 + b2 sin(ωx + φ) + B .
5. With the help of your classmates, express the domains of the functions in Examples 10.5.4
and 10.5.5 using extended interval notation. (We will revisit this in Section 10.7.) 692 Foundations of Trigonometry 6. Graph the following functions with the help of your calculator and discuss the given questions
with your cla...
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