Mid-Chapter Quiz
Sign In
Rewrite 5π12 as π4+ π6. Then, use the Sum of Angles Identity for a cosine function.
H
We want to find the exact value of cos 5Ï€12. To do so, we can use the Sum of Angles Identity for a cosine function. Before we rewrite the given expression, let's start by recalling the values of the three main trigonometric functions for the most important angles.
| sin θ | cos θ | tan θ | |
|---|---|---|---|
| θ =0 | 0 | 1 | 0 |
| θ =π/6 | 1/2 | sqrt(3)/2 | sqrt(3)/3 |
| θ =π/4 | sqrt(2)/2 | sqrt(2)/2 | 1 |
| θ =π/3 | sqrt(3)/2 | 1/2 | sqrt(3) |
| θ =π/2 | 1 | 0 | - |
| θ =π | 0 | - 1 | 0 |
| θ =2π | 0 | 1 | 0 |
Let's now recall the Sum of Angles Identity for a cosine function.
Write as a sum
Distribute π
Write as a sum of fractions
a/b=.a /3./.b /3.
a/b=.a /2./.b /2.
cos ( A+ B)= cosA cos B-sinAsin B
Next, we will use the table we constructed at the beginning of this solution to find the exact value of the expression. cos π/4 cos π/6 - sin π/4 sin π/6 ⇕ sqrt(2)/2 (sqrt(3)/2)- sqrt(2)/2 (1/2) Let's finally simplify the obtained expression!
Therefore, the correct answer is H.