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

###

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

###

14. Simplification follows from the definitions of each function:

So we have

###

15. Use the Pythagorean identity:

Then

i think there was a typo. you wrote pat brings 3 quarts of ice-cream to the party. each serving of ice-cream is 1 6 quart. how many total servings of ice-cream does pat bring to the party? i think the bold is supposed to be 1/6. so 1 quart of ice cream = 6 servings. 6 * 3 = 18.

idk

step-by-step explanation: