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

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

...