Question

5.3
score: 8/22 answered: 8/22
question 9
find the exact value of the expression.
\\( \tan \left( \frac { \pi } { 4 } \
ight) = \\)

Explanation:

Step1: Recall the tangent formula

$\tan\theta=\frac{\sin\theta}{\cos\theta}$. For $\theta = \frac{\pi}{4}$, we know that $\sin\frac{\pi}{4}=\frac{\sqrt{2}}{2}$ and $\cos\frac{\pi}{4}=\frac{\sqrt{2}}{2}$.

Step2: Calculate the value

Substitute the values of $\sin\frac{\pi}{4}$ and $\cos\frac{\pi}{4}$ into the tangent formula: $\tan\frac{\pi}{4}=\frac{\sin\frac{\pi}{4}}{\cos\frac{\pi}{4}}=\frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1$.

Answer:

$1$