Hello, Glitch!
The book's answer is wrong . . .
Find the domain of: .
Use inequalities . . .
. .
If is between and
. . then is basically between and
Therefore: .
The question:
Find the domain of:
My attempt:
I worked out that x = 30 degrees, or Pi/6
So I want the values where sinx is larger than or equal to 1/2:
Where k is an integer.
I thought this made sense, but the answer in my book is:
What am I doing wrong? :/
Hi,
Glitch, Your solution is where the sine is greater than or equal to 1/2! Infact you should find the angles which their sine is less than or equal to 1/2.
The simplest way is to use a unit circle or a sine graph to solve this Trigonometric inequality.
1-Draw a unit circle.
2-Draw a horizontal line to cosine axis such that intersects the sine axis at the point 1/2.
3-Since at the 1st and 2nd quadrants sine is 1/2 at pi/6 and pi-pi/6=5pi/6, the line intersects the circle at those points. Now you can see that all the angles between pi/6 and 5pi/6 have sines greater than 1/2. So what interval do you think you should takeas solution?
Therefore you can see that the book's solution is true! (Note that -7pi/6 is in the same location of 5pi/6 and so they have the equal Trig relationships)