Question

given that sin alpha = root 3/2 and cos beeta = 0 then find the Value of beta - alpha ​

Answer 1

Answer:

Step-by-step explanation:

given ,

sin α = √3/2 = sin 60

cos β = 0 = cos 90

β -  α = 90 - 60 = 30

hope this answer could help you :)

Answer 2

Given data: $sin\alpha ={\frac{\sqrt{3} }{2 }$ and $cos \beta =0$

To Find: $\beta -\alpha$

Solution:

To find the value of $\alpha$, consider $sin\alpha ={\frac{\sqrt{3} }{2 }$

By using trignometric table, the standard angle can be found.

The values of, $sin$ $0$°$=0$, $sin$ $30$°$=\frac{1}{2}$, $sin$ $45$°$=\frac{1}{\sqrt{2} }$, $sin$ $60$°$={\frac{\sqrt{3} }{2} }$, $sin$ $90$°$=1$.

Hence, $sin$ $60$°$={\frac{\sqrt{3} }{2} }$  

$\alpha =60$°

To find the value of $\beta$,

Consider $cos\beta =0$

From the trignometric table, the standard angle can be found.

The value of, $cos$ $0$°$=1$, $cos$ $30$°$=\frac{\sqrt{3} }{2}$, $cos$ $45$°$=\frac{1}{\sqrt{2} }$, $cos$ $60$°$=\frac{1}{2}$, $cos$ $90$°$=0$.

Hence, $cos$ $90$°$=0$

$\beta =$$90$°

$\beta -\alpha$$=90$°$-60$°

$\beta -\alpha =$ $30$°

Therefore, the value of $\beta -\alpha =$ $30$°.