6. To distinguish between a Relation and a Function.
7. To verify the relation between the degree measure and the radian measure of an angle.
8. To find the values of sine and cosine functions in second, third and fourth quadrants using their given values in first quadrant.
Answer (1)
Distinguishing between a Relation and a Function :
A relation in mathematics is a set of ordered pairs, usually defined as any connection or association between two sets of values. For example, (2,3), (4,5), and (6,9) can be a relation.
A function is a specific type of relation where each element in the domain is associated with exactly one element in the codomain. This means that for a function, no two ordered pairs have the same first element and different second elements. For example, the relation (2,3), (4,5), and (6,9) is a function because every first element is paired with only one second element.
Verifying the Relation between Degree and Radian Measure of an Angle :
The degree and radian are two units for measuring angles. They are related to each other in that 180 degrees is equivalent to π radians. The formula to convert degrees to radians is:
Radians = Degrees × 180 π
To convert radians to degrees, use:
Degrees = Radians × π 180
Finding Values of Sine and Cosine Functions in Different Quadrants :
The sine and cosine functions have specific sign changes as you move through the quadrants:
In the first quadrant (0 to 90 degrees or 0 to 2 π radians), both sine and cosine are positive.
In the second quadrant (90 to 180 degrees or 2 π to π radians), sine is positive while cosine is negative.
In the third quadrant (180 to 270 degrees or π to 2 3 π radians), both sine and cosine are negative.
In the fourth quadrant (270 to 360 degrees or 2 3 π to 2 π radians), sine is negative while cosine is positive.
Therefore, if you know the values of sine and cosine in the first quadrant, you can determine their absolute values in other quadrants and apply the respective sign rules based on the quadrant's characteristics.
