Solving Basic Trig Equations

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Solve for x over the interval

$0\le x<2\pi$

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Solve for ALL values of x:

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Solve for ALL values of x:

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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.

For what numbers x, 0 e x e2 \pi, does sin x =1

• π/2, 3π/2

• π/2

• 0, 2

• none

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

• π/2, 3π/2

• π/2

• 0, 2

• none

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

• π/2, 3π/2

• π/2

• 0, 2

• none

Let's solve for all solutions from 0 to the end of one period of the function. That interval would be 0≤x<2π/3. We would get 3x=​ (a)   and 3x=​ (b)