Precalc - trig identities. decent explanation, .

12. Recall the half-angle identity,

where we take the positive square root because is an angle in a right triangle, which means , so . For such an angle, it's always the case that .

Use the Pythagorean theorem to find the length of the hypotenuse:

Then

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13. is in quadrant II, which means , so . In other words, is in quadrant I, so . From the half-angle identity we get

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14. Simplification follows from the definitions of each function:

So we have

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15. Use the Pythagorean identity:

Then

hope it

step-by-step explanation:

x^(1/6) · x^(1/6) · x^(1/6)   ·x^(1/6) = x^(4/6)   since we add the exponents

4/6 can be simplified to 2/3

the simplified form is x^(2/3)

step-by-step explanation:

ok one would be money, and the other would be refreshments or something similar. if each bag of popcorn is 5.00 and each drink is half of that that means drinks are 2.50 the proper way to do that would to look and see how much of each you can buy without exceeding a limit of 30.00