3. Find the exact value of the following expressions

a)

Using the half angle identity and choosing the plus sign since the angle 15 is in Quadrant I where the sine is positive.

b)

Using the cofunction identity:

and

As above

Thus,

c)

5. Prove that

Therefore

Math 002-041

Cal Problems Solution 6.1-6.2

A. Farhat

1. Verify the following identities

a)

Using the property that the sine function is odd and the cosine function is even.

Factor the difference of two squares.

Cancel [sin(x) + cos(x)]

b)

and

Using the figures on the right, we have

Thus,

Using the cofunction property

2. If , a in Quadrant II, and , b in Quadrant II, then find

Since both the numerator and the denominator are positive if x is in the first quadrant.