Solving Simple Trig Equations

Find all the solutions [0, 2π) for this equation: sin x = 1/2

• π/3

• π/6

• 5π/6

• 11π/6

• 2π/3

Find all the solutions [0, 2π) for this equation: 2sin x +√3 = 0

• π/3

• 2π/3

• 5π/6

• 4π/3

• 5π/3

Find all the solutions [0, 2π) for this equation:

5sin x +1 = 3sin x

• π/6

• 5π/6

• 7π/6

• not this one

• 11π/6

Find all the solutions [0, 2π) for this equation:

7cos x -9 = -2cos x

• 0

• π/2

• π

• 3π/2

• 2π (it can't be this one knuckleheads)

If sinΘ=1/2, what does theta equal? There are two answers, put the smaller answer first (a)   and ​ (b)  

• 30

• 150

• 45

• 60

• 90

• 120

• 135

• 180

• 210

• 225

Answer explanation

sine correlates with y and there are two points that have a y value of 1/2. 30 and 150 degrees.

Let's solve for all solutions from 0 to the end of one period of the function.

That interval would be 0≤x<___

Mathematical Equivalence

ON

Solve for ALL values of x (from least to greatest): x=​ ​ (a)   + 2πn &​ (b)   +2πn

• π/4

• 7π/4

• 3π/4

• 5π/4

• π/3

• 2π/3

• 4π/3

• 5π/3

• 0

• π

For what numbers x, 0 e x e2 ext{π} , does sin x= -1

• π/2, 3π/2

• 3π/2

• none

For what numbers x, 0≤x≤2π, does sin x =1

• π/2, 3π/2

• π/2

• 0, 2

• none