cos 80°
0.174
The value of cos 80° can be determined using any of the following methods:
1) Using a calculator:
We can directly input cos 80° in a scientific calculator and get its value as 0.17364817766693.
2) Using the angle sum formula:
cos 80° = cos (60° + 20°)
= cos 60° cos 20° – sin 60° sin 20° *[From the angle sum formula for cosine function]
Now, we know that cos 60° = 1/2 and sin 60° = √3/2 (which can be derived from the unit circle or trigonometric ratios).
Substituting these values, we get:
cos 80° = (1/2) cos 20° – (√3/2) sin 20°
Again, we need to know the value of cos 20° and sin 20° to simplify it further. We can either use a table of values or a calculator to find them.
cos 20° = 0.93969262078591
sin 20° = 0.34202014332567
Substituting these values, we get:
cos 80° = (1/2) (0.93969262078591) – (√3/2) (0.34202014332567)
= 0.17364817766693
Therefore, the value of cos 80° is 0.17364817766693 (rounded to 14 decimal places).
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