Use a half angle identity to find the exact value- sin(75 degrees)

Solution:

The line of a half angle identity is as follows:

If we plug in 75 degrees we get:

Find the descriminant of x^2-7x+2=0 and describe the natural roots

Solution:

1. When you have an equation in the form of ax² + =x + c = 0, the solution is x = where  D = b² – 4ac
2. D stands for discriminant, and values of x are the natural roots

• If D > 0, then the values of x are real and distinct.

• If D = 0, then the values of x are real and equal

• If D < 0, then the values of x are unreal

1. In your question, x² – 7x + 2 = 0, so the values of a, b and c are as follows:

• a = 1

• b = -7

• c = 2

1. D = b² – 4ac = 49 – 8 = 41 (this is the value of the discriminant)
2. Since D > 0, then the values of x (the natural roots) are real and distinct