Add/Subrtraction Trig Formulas

[kelleynicole30]

Find the exact value. (We are suppost to use the trig add/subtraction formulas to solve.)

cos75degrees (use 75deg =135deg - 60deg)


I got the answer (-sqr root(2) + sqr root(6))/4 is this correct? If not please show how to solve. Thanks.

 

[masters]

Find the exact value. (We are suppost to use the trig add/subtraction formulas to solve.)

cos75degrees (use 75deg =135deg - 60deg)


I got the answer ((-sqr root(2) + sqr root(6))/4 is this correct? If not please show how to solve. Thanks.

Looks good to me.

 

[soroban]

Hello, kelleynicole30!

Find the exact value: .\(\displaystyle \cos(75^o)\)

Some friendly advice . . . Use the smallest possible positive angles.


\(\displaystyle \cos(75^o) \;=\;\cos(45^o+30^o)\)

. . . . . . .\(\displaystyle = \;\cos(45^o)\cos(30^o) - \sin(45^o)(\sin30^o)\)

. . . . . . .\(\displaystyle = \;\;\;\left(\frac{\sqrt{2}}{2}\right)\left(\frac{\sqrt{3}}{2}\right) - \left(\frac{\sqrt{2}}{2}\right)\left(\frac{1}{2}\right)\)

. . . . . . .\(\displaystyle = \quad\frac{\sqrt{6}}{4} - \frac{\sqrt{2}}{4}\)

. . . . . . .\(\displaystyle =\quad\frac{\sqrt{6}-\sqrt{2}}{4}\)