Question

What is the exact value of cos (67.5° )?

Answer 1

Answer:

0.38268343

Step-by-step explanation:

cos( 67.5 )

Rewrite  

67.5

as an angle where the values of the six trigonometric functions are known divided by  2 . cos ( 135\ 2)

Apply the cosine half-angle identity.

±

√

1

+

cos

(

135

)

2

 

Change the  

±

to  

+

because cosine is positive in the first quadrant.

√

1

+

cos

(

135

)

2

Simplify  

√

1

+

cos

(

135

)

2

√

2

−

√

2

2

The result can be shown in multiple forms.

Exact Form:

√

2

−

√

2

2

Decimal Form:

0.38268343

…