Download HW1 1. Given that 3sin x + 4 cosx = 5 find sin x,cosx 2. Find k such

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HW1
1. Given that 3 sin x + 4 cos x = 5 find sin x, cos x
2. Find k such that the expression (sin x + cos x)2 + k sin x cos x = 1 becomes an
identity.
3. If sin x + cos x =
1
and x ∈ (0, π) find cos x and sin x.
5
4. Find the minimum value of the function
f (x) =
9x2 sin2 x + 4
x sin x
over the interval x ∈ (0, π)
5. Give a graphical argument justifying the inequality
2x
π
≤ sin x for 0 ≤ x ≤
π
2
6. Give a purely graphical argument (no calculators allowed!) justifying cos 1 < sin 1.
7. For which real numbers x is logcos x x a real number
8. Find the period of sin 2x + cos 3x
9. How many real numbers x satisfy
sin x =
1
x
100
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