With the help of tables, find the values, correct to places of decimals, of each of the following :
`cos116^(@)`

Answer

To find the value of \( \cos 116^\circ \) using trigonometric identities and tables, we can follow these steps:

### Step 1: Rewrite the angle
We can express \( \cos 116^\circ \) in terms of a related angle. Since \( 116^\circ \) is in the second quadrant, we can use the identity:
\[ \cos(90^\circ + \theta) = -\sin(\theta) \]
Here, we can set \( \theta = 26^\circ \) because \( 116^\circ = 90^\circ + 26^\circ \).

### Step 2: Apply the identity
Using the identity from Step 1, we can write:
\[ \cos 116^\circ = \cos(90^\circ + 26^\circ) = -\sin(26^\circ) \]

### Step 3: Find \( \sin 26^\circ \) from the table
Now, we need to look up the value of \( \sin 26^\circ \) in the trigonometric tables. From the tables, we find:
\[ \sin 26^\circ \approx 0.4384 \]

### Step 4: Substitute the value
Now we substitute this value back into our equation from Step 2:
\[ \cos 116^\circ = -\sin(26^\circ) = -0.4384 \]

### Step 5: Final answer
Thus, the value of \( \cos 116^\circ \) is:
\[ \cos 116^\circ \approx -0.4384 \]