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Trigonometric equations from a to x, featuring functions like sin, cos, tan, and cot with different variables and constants.

A list of trigonometric equations labeled a through x, including sine, cosine, tangent, and cotangent functions with various arguments and constants.

A list of trigonometric equations labeled a through x, including sine, cosine, tangent, and cotangent functions with various arguments and constants.

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Show Answer Key & Explanations Step-by-step solution for: Math Exercises & Math Problems: Trigonometric Equations and ...
a) x = π/10 + 2πk/5, k ∈ ℤ
b) x = π/4 + πk/2, k ∈ ℤ
c) x = π/9 + πk/3, k ∈ ℤ
d) x = π + 2πk, k ∈ ℤ
e) x = -3π/4 + 6πk or x = 3π/4 + 6πk, k ∈ ℤ
f) x = 4π + 8πk, k ∈ ℤ
g) x = (2π/3 - 1)/3 + 2πk/3 or x = (4π/3 - 1)/3 + 2πk/3, k ∈ ℤ
h) x = -π + 4πk, k ∈ ℤ
i) x = (4π/3 + 1)/3 + πk/3, k ∈ ℤ
j) x = 2π/3 - π/6 + 2πk or x = 4π/3 - π/6 + 2πk, k ∈ ℤ
k) x = 3π/4 + 6πk or x = 9π/4 + 6πk, k ∈ ℤ
l) x = 5π/8 + πk/2, k ∈ ℤ
m) x = (π/6 + 1)/4 + πk/2, k ∈ ℤ
n) x = 4π/3 + 12πk or x = 8π/3 + 12πk, k ∈ ℤ
o) x = -π/3 + 2πk, k ∈ ℤ
p) x = π/2 - 4 + 8πk or x = 3π/2 - 4 + 8πk, k ∈ ℤ
q) x = -3π/2 + 4πk, k ∈ ℤ
r) cos(3x) = 0 or cos(3x) = 1/√2; x = π/6 + πk/3 or x = π/12 + 2πk/3 or x = -π/12 + 2πk/3, k ∈ ℤ
s) sin(x) = 0 or cos(x) = -1/2; x = πk or x = 2π/3 + 2πk or x = 4π/3 + 2πk, k ∈ ℤ
t) sin²(x) = 1/2; x = π/4 + πk/2, k ∈ ℤ
u) cos(x) = -1/2; x = 2π/3 + 2πk or x = 4π/3 + 2πk, k ∈ ℤ
v) sin(x) - cos(x) = 1; x = π/2 + 2πk or x = π + 2πk, k ∈ ℤ
w) tan(x) = 0 or tan(x) = 1; x = πk or x = π/4 + πk, k ∈ ℤ
x) sin(x) = 0 or cos(x) = 1/2; x = πk or x = π/3 + 2πk or x = 5π/3 + 2πk, k ∈ ℤ
Parent Tip: Review the logic above to help your child master the concept of solving trig equations worksheet.
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