Solve sin x=1/2 on [0,2π).
Answer: x=π/6,5π/6
Reasoning: Sine is positive in Quadrants I and II.
Reasoning: Sine is positive in Quadrants I and II.
Teacher Key · Unit 06 · Lesson 07
Solving Multi-Step Equations on Intervals
Use this key to verify method, notation, domain, units, and interpretation. Accept equivalent exact forms when mathematically valid.
Khaemenes Academy · Teacher Key
Solving Multi-Step Equations on Intervals
Solve cos x=−√2/2 on [0,2π).
Answer: x=3π/4,5π/4
Reasoning: Cosine is negative in Quadrants II and III.
Reasoning: Cosine is negative in Quadrants II and III.
Solve tan x=1 on [0,2π).
Answer: x=π/4,5π/4
Reasoning: Tangent has period π.
Reasoning: Tangent has period π.
Solve 2sin x−1=0 on [0,2π).
Answer: x=π/6,5π/6
Reasoning: Reduce to sin x=1/2.
Reasoning: Reduce to sin x=1/2.
Give the general solution of cos x=1.
Answer: x=2πn
Reasoning: Cosine equals one at full turns.
Reasoning: Cosine equals one at full turns.
Why must solutions be checked after squaring an equation?
Answer: Squaring may create extraneous solutions
Reasoning: The reverse implication need not hold.
Reasoning: The reverse implication need not hold.