# How do you find the exact value of #cos ((2pi)/9) cos (pi/18)+sin ((2pi)/9) sin (pi/18)#?

By signing up, you agree to our Terms of Service and Privacy Policy

The above expression simplifies to

By signing up, you agree to our Terms of Service and Privacy Policy

You can use the cosine of the difference formula ( \cos(A - B) = \cos A \cos B + \sin A \sin B ) to find the exact value of ( \cos\left(\frac{2\pi}{9}\right) \cos\left(\frac{\pi}{18}\right) + \sin\left(\frac{2\pi}{9}\right) \sin\left(\frac{\pi}{18}\right) ).

Using the given angles ( \frac{2\pi}{9} ) and ( \frac{\pi}{18} ):

[ \cos\left(\frac{2\pi}{9} - \frac{\pi}{18}\right) ]

[ = \cos\left(\frac{4\pi}{18} - \frac{\pi}{18}\right) ]

[ = \cos\left(\frac{3\pi}{18}\right) ]

[ = \cos\left(\frac{\pi}{6}\right) ]

[ = \frac{\sqrt{3}}{2} ]

So, the exact value is ( \frac{\sqrt{3}}{2} ).

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you solve #sec(tan^-1x) = sqrt(1+x^2)#?
- What is the length of the hypotenuse of a right triangle if the two other sides are of lengths 5 and 14?
- How do you find leg length, BC, to the nearest tenth if in a right triangle ABC, the hypotenuse #AB=15# and angle #A=35º#?
- If #tanx=4# and #x# lies in the interval #0^@ < x<90^@#, what is #sec^2x#?
- Why do you need to use special right triangles?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7