Question

Write the expression as either the sine, cosine, or tangent of a single angle. sin(pi/2)cos(pi/7)+cos(pi/2)sin(pi/7)

Answer 1

I will use the sin (a + b) identity: 
sin (a + b) = sina cosb + cosa sinb and
here a = π/2 and b = π/7 

so sin (π/2 + π/7) 
= sin (9π / 14)

Answer 2

Answer:

$\text{sin}(\frac{9\pi}{14})$.

Step-by-step explanation:

We have been given a trigonometric expression $\text{sin}(\frac{\pi}{2})\text{cos}(\frac{\pi}{7})+\text{cos}(\frac{\pi}{2})\text{sin}(\frac{\pi}{7})$. We are asked to write our given expression as either the sine, cosine, or tangent of a single angle.

Using identity $\text{sin}(a)\text{cos}(b)+\text{cos}(a)\text{sin}(b)=\text{sin}(a+b)$, we can rewrite our given expression.

Let $a=\frac{\pi}{2}$ and $b=\frac{\pi}{7}$.

Upon substituting these values in above identity, we will get:

$\text{sin}(\frac{\pi}{2})\text{cos}(\frac{\pi}{7})+\text{cos}(\frac{\pi}{2})\text{sin}(\frac{\pi}{7})=\text{sin}(\frac{\pi}{2}+\frac{\pi}{7})$

Upon simplifying right side of our equation, we will get:

$\text{sin}(\frac{\pi}{2}+\frac{\pi}{7})=\text{sin}(\frac{\pi*7}{2*7}+\frac{\pi*2}{7*2})$

$\text{sin}(\frac{\pi}{2}+\frac{\pi}{7})=\text{sin}(\frac{7\pi}{14}+\frac{2\pi}{14})$

$\text{sin}(\frac{\pi}{2}+\frac{\pi}{7})=\text{sin}(\frac{7\pi+2\pi}{14})$

$\text{sin}(\frac{\pi}{2}+\frac{\pi}{7})=\text{sin}(\frac{9\pi}{14})$

Therefore, our required expression would be $\text{sin}(\frac{9\pi}{14})$.