What you REALLY need to get down for test 3

Question 1

cos(α/2)

Answer 1

± √((1 + cosα)/2)

Question 2

tan(α/2)

Answer 2

± sinα/(1 + cosα)

Question 3

sin(α/2)

Answer 3

± √((1 - cosα)/2)

Question 4

tan2θ

Answer 4

(2tan)/(1-tan²)

Question 5

cos2θ from sin

Answer 5

1 - 2sin²

Question 6

cos2θ from cos

Answer 6

2cos² - 1

Question 7

how to get 1 from cot & csc

Answer 7

csc² - cot²

Question 8

how to get 1 from tan & sec

Answer 8

sec² - tan²

Question 9

What is the trick that Mr. Adams likes to use for making rectangular equations about sin & cos, and sec & tan

Answer 9

Don’t isolate t all the way. if it looks like 7cost = x and 8sint = y, just isolate the trig function and t, so like:
cost = x/7, sint = y/8.
Then put the Pythagorean property, sin² + cos² = 1, on it by squaring what cost and sint equals: x²/49 + y²/64 = 1

Question 10

When you’re told to make 2 different parametric equations, what 2 values should you write x equal to, and then work both into the original equation?

Answer 10

set x = t and x = (t - 1). Then put it into x in the equation and simplify. You’ll be fine

Question 11

in the half-angle formulas, what does ± mean when it comes in front of the formula?

Answer 11

it means that depending on which quadrant the angle is in, it determines if it’s positive or negative. It could be either. so like, if it asks for the sin of a positive tan angle in Q3, the ± would translate to a negative value of the formula bc it’s asking for sin, not tan.

Question 12

what are the 3 pairs of trig fn’s that mr adams likes to use for his parametric equation rectangular equation trick?

Answer 12

sin & cos, and sec & tan, and csc & cot. Basically all the ones that can be derived from the pythagorean properties