Find the exact value for cos π 12 applying sum and difference formulas involving π 3 and π 4 .

First, split the angle into two angles where the values of the six trigonometric functions are known. In this case, π/12 can be split into π/3−π/4.

cos(π/3−π/4)

Use the difference formula for cosine to simplify the expression. The formula states that cos(A−B)=cos(A)cos(B)+sin(A)sin(B)

cos(π/3)⋅cos(π/4)+sin(π/3)⋅sin(π/4)

The exact value of cos(π/3) is 12, so:

(12)⋅cos(π/4)+sin(π/3)⋅sin(π/4)

The exact value of cos(π/4) is √22.

(12)⋅(√22)+sin(π/3)⋅sin(π/4)

The exact value of sin(π/3) is √32.

(12)⋅(√22)+(√32)⋅sin(π/4)

The exact value of sin(π/4) is √22.

(12)⋅(√22)+(√32)⋅(√22)

Simplify each term:

√24+√64

Combine the numerators over the common denominator.

(√2+√6) / 4

exa:

)

3+11

14

step-by-step explanation:

from this example, we can see that subtracting with integers is the same as adding the opposite. we can solve using a number line or by using the saying "keep, change, change" to us solve. it is important to remember that we can subtract a negative and end up with a larger number than we started with.

hi there!

first we need to find out how much they are adding to each number to make the next number.

ex: 4 + 4 = 8, 8 + 8 = 16, and so on.

so continuing with 32,

32 + 32 = 64

64 + 64 = 128

128 + 128 = 256

256 + 256 = 512

4, 8, 16, 32, 64, 128, 256, 512

the 8th term of the sequence will be 512

hope this ! ~