Answer:
Step-by-step explanation:
There are multiple ways to achieve and even express the exact answer to this problem. Because the exact value of is a non-terminating (never-ending) decimal, it does not have a finite number of digits. Therefore, you cannot express it as an exact value as a decimal, as you'd either have to round or truncate.
<u>Solution 1 (Cosine Addition Identity):</u>
Nonetheless, to find the exact value we must use trigonometry identities.
Identity used:
Notice that and therefore we can easily solve this problem if we know values of , , , and , which is plausible as they are all key angles on the unit circle.
Recall from either memory or the unit circle that:
Therefore, we have:
Since we want the value of , simply multiply this by 6 to get your final answer:
<u>Solution 2 (Combination of trig. identities):</u>
Although less plausible, you may have the following memorized:
If so, we can use the following trig. identity:
(the cosine of angle theta is equal to the sine of the supplement of angle theta - the converse is also true)
Therefore,
Recall another trig. identity:
and therefore:
Multiply by 6 to get:
(alternative final answer).