Please help me with this trig question

[ryan882]

Hi im new to this forum
can anyone help me to find the exact value of this question. I know its easy but..

If cosA= 3/4 ,Find the exact value of cos1/2A. ?

 

[serds]

Try:

1. cos^-1 (0.75)= A
2. A:2
3. cos (A/2)

 

[HallsofIvy]

Hi im new to this forum
can anyone help me to find the exact value of this question. I know its easy but..

If cosA= 3/4 ,Find the exact value of cos1/2A. ?

I imagine that whoever gave you this problem expects you to know the "half angle formula"
\(\displaystyle cos(\frac{A}{2})= \pm\sqrt{\frac{1}{2}(1+ cos(A)}\). Of course to give the exact value, you would have to have more information. For example, if cos(A)= 1/2, then cos(A/2) may be \(\displaystyle \frac{\sqrt{3}}{2}\) (\(\displaystyle A= \frac{\pi}{3}\) radians) or \(\displaystyle -\frac{\sqrt{3}}{2}\) (\(\displaystyle A= \frac{5\pi}{3}\) radians).

 

[srmichael]

Hi im new to this forum
can anyone help me to find the exact value of this question. I know its easy but..

If cosA= 3/4 ,Find the exact value of cos1/2A. ?

Like HOI mentioned, high likelihood you are supposed to know the half angle formulas. That being said:

\(\displaystyle cos(\dfrac{A}{2})= \pm\sqrt{\dfrac{1}{2}(1+ cos(A)}\)

\(\displaystyle = \pm\sqrt{\dfrac{1}{2}(1+ \dfrac{3}{4})}\)

Can you take it from here?

 

[ryan882]

I imagine that whoever gave you this problem expects you to know the "half angle formula"
\(\displaystyle cos(\frac{A}{2})= \pm\sqrt{\frac{1}{2}(1+ cos(A)}\). Of course to give the exact value, you would have to have more information. For example, if cos(A)= 1/2, then cos(A/2) may be \(\displaystyle \frac{\sqrt{3}}{2}\) (\(\displaystyle A= \frac{\pi}{3}\) radians) or \(\displaystyle -\frac{\sqrt{3}}{2}\) (\(\displaystyle A= \frac{5\pi}{3}\) radians).

Thank you very much for the help. I didnt knew that formula till now it really helped me

 

[ryan882]

Like HOI mentioned, high likelihood you are supposed to know the half angle formulas. That being said:

\(\displaystyle cos(\dfrac{A}{2})= \pm\sqrt{\dfrac{1}{2}(1+ cos(A)}\)

\(\displaystyle = \pm\sqrt{\dfrac{1}{2}(1+ \dfrac{3}{4})}\)

Can you take it from here?

Thank you very much for the help yes now i can take it from here