Find Exact Value of Trigonometric Expression...1

[nycmathguy]

Section 5.4

1. Is there a shorter method that can be used? This is pretty tedious.

2. Is my answer correct?

 

[MathLover1]

1. yes, there is a shorter method

use Angle-Sum and -Difference Identities

sin(α + β) = sin(α) cos(β) + cos(α) sin(β)

in your case α=pi/12 and β=pi/4

sin(pi/12)cos(pi/4)+cos(pi/12)sin(pi/4)
=sin(pi/12 + pi/4)
=sin(π/3)
=sqrt(3)/2

2. as you can see, your answer is not correct

 

[nycmathguy]

1. yes, there is a shorter method

use Angle-Sum and -Difference Identities

sin(α + β) = sin(α) cos(β) + cos(α) sin(β)

in your case α=pi/12 and β=pi/4

sin(pi/12)cos(pi/4)+cos(pi/12)sin(pi/4)
=sin(pi/12 + pi/4)
=sin(π/3)
=sqrt(3)/2

2. as you can see, your answer is not correct

Ok. Thanks. I will do at least 2 more and post my work here.

Christmas is here again. May your home be filled with laughter, contentment, harmony, peace, and an abundance of mercy. Happy holidays.

 

[nycmathguy]

1. yes, there is a shorter method

use Angle-Sum and -Difference Identities

sin(α + β) = sin(α) cos(β) + cos(α) sin(β)

in your case α=pi/12 and β=pi/4

sin(pi/12)cos(pi/4)+cos(pi/12)sin(pi/4)
=sin(pi/12 + pi/4)
=sin(π/3)
=sqrt(3)/2

2. as you can see, your answer is not correct

Take a look at 36.

 

[MathLover1]

correct

 

[nycmathguy]

correct

Very good. Thank you.