To solve trigonometric inequalities using the unit circle, we need to understand how trigonometric functions—like sine, cosine, and tangent—act for different angles.
Let’s start with an example inequality: .
This means we want to find out where the sine function is positive (greater than 0) but also less than 1.
On the unit circle, we can see where the sine value (which is the y-coordinate) fits within our criteria.
The sine function is positive in the first and second quadrants of the unit circle.
In the case of , we can look at the angles:
Now, let's write down these intervals:
Trigonometric functions repeat their values. So, for any whole number , we can express this as: This means we can find all the answers within each repeating cycle.
Using the unit circle helps us to easily see and solve these inequalities!
To solve trigonometric inequalities using the unit circle, we need to understand how trigonometric functions—like sine, cosine, and tangent—act for different angles.
Let’s start with an example inequality: .
This means we want to find out where the sine function is positive (greater than 0) but also less than 1.
On the unit circle, we can see where the sine value (which is the y-coordinate) fits within our criteria.
The sine function is positive in the first and second quadrants of the unit circle.
In the case of , we can look at the angles:
Now, let's write down these intervals:
Trigonometric functions repeat their values. So, for any whole number , we can express this as: This means we can find all the answers within each repeating cycle.
Using the unit circle helps us to easily see and solve these inequalities!