Homework

Problem 1 · easy

Simplify: cos(x)*tan(x).

Problem 2 · easy

Simplify: (sec^2(x) - 1)/tan^2(x).

Problem 3 · medium

Simplify: sin^2(x)*cot^2(x).

Problem 4 · medium

Simplify: (sin(x) + cos(x))^2.

Problem 5 · challenge

Prove: (1+sin(x))/cos(x) + cos(x)/(1+sin(x)) = 2*sec(x). (Show the steps.)

Problem 6 · medium

Find cos(15°) using the difference formula.

Problem 7 · medium

Find sin(75°) using the sum formula.

Problem 8 · challenge

Find tan(π/12) using the difference formula. (π/12 = π/3 - π/4)

Problem 9 · medium

If sin(A) = 4/5 and A is in QI, find sin(2A).

Problem 10 · medium

If cos(A) = -1/3 and A is in QII, find cos(2A).

Problem 11 · medium

Solve on [0, 2π): 2*cos(x) + sqrt(2) = 0.

Problem 12 · medium

Solve on [0, 2π): tan(x) = sqrt(3).

Problem 13 · medium

Solve on [0, 2π): 2*sin^2(x) + sin(x) - 1 = 0.

Problem 14 · medium

Solve on [0, 2π): sin(2x) = 0.

Problem 15 · medium

Find all solutions: sin(x) = -1/2.

Problem 16 · easy

Find all solutions: cos(x) = 0.

Problem 17 · challenge

Solve on [0, 2π): cos(2x) = 1/2.

Problem 18 · medium

Simplify using double-angle: sin(2x)/cos(x).

Problem 19 · challenge

Use the formula to find cos(π/12). (π/12 = π/3 - π/4)

Problem 20 · medium

Verify: sin(A+B) - sin(A-B) = 2*cos(A)*sin(B). Show two or three algebraic steps.

Problem 21 · challenge

Solve on [0, 2π): sin(x)*cos(x) = 1/4.

Problem 22 · easy

State cos(2x) in terms of sin(x) only.

Problem 23 · medium

Solve on [0, 2π): 2*sin^2(x) - 3*sin(x) + 1 = 0.

Problem 24 · medium

Prove: sec(x) - cos(x) = sin(x)*tan(x). Work the left side.

Problem 25 · challenge

Find sin(π/12) using the half-angle formula for π/6.