Test 3

Question 1

how to get 1 from sin & cos

Answer 1

1 = sin² + cos²

Question 2

how to get 1 from sec & tan

Answer 2

1 = sec² - tan²

Question 3

how to get tan from sin & cos

Answer 3

tan = sin/cos

Question 4

how to get cot from sin & cos

Answer 4

cot = cos/sin

Question 5

cos(α + β)

Answer 5

cosαcosβ - sinαsinβ

Question 6

cos(α - β)

Answer 6

cosαcosβ + sinαsinβ

Question 7

sin(α + β)

Answer 7

sinαcosβ + cosαsinβ

Question 8

sin(α - β)

Answer 8

sinαcosβ - cosαsinβ

Question 9

tan(α + β)

Answer 9

(tanα + tanβ)/(1 - tanαtanβ)

Question 10

tan(α - β)

Answer 10

(tanα - tanβ)/(1 + tanαtanβ)

Question 11

sin2θ

Answer 11

2sincos

Question 12

cos2θ with sin & cos

Answer 12

cos² - sin²

Question 13

sin(α/2)

Answer 13

± √((1 - cosα)/2)

Question 14

cos(α/2)

Answer 14

± √((1 + cosα)/2)

Question 15

tan(α/2)

Answer 15

± sinα/(1 + cosα)

Question 16

cos2θ with sin

Answer 16

1 - 2sin²

Question 17

cos2θ with cos

Answer 17

2cos² - 1

Question 18

how to go about solving for (trig fⁿ)² = ratio

Answer 18

a) answer it as ±(trig fⁿ)⁻¹(ratio)

b) then you will have 4 answers all around the Q’s

Question 19

how to go about solving for (trig fⁿ)(nθ) = ratio

Answer 19

a) Find the 2 angles θ would be without division.
b) Write out 2 formulas that look like this: 2θ = (angle 1 or 2) + 2πk
c) Divide and get θ = (angle 1 or 2)/2 + πk
d) Keep adding πk to each of the 2 angles until you reach below the limit θ has to be in

Question 20

how to go about solving for (trig fⁿ) = decimal in a certain quadrant

Answer 20

a) Find the sign of the trig fⁿ when it’s in the quadrant you have to solve for
b) Plug (trig fⁿ)⁻¹(decimal) into calc to find your first answer, θ
c) Subtract θ from π if the same-sign value is on top; subtract it from 2π if the same-sign value is on bottom.

Question 21

how to go about solving for (trig fⁿ) = (different trig fⁿ)

Answer 21

a) Try to turn them into multiples by manipulating the equation
b) Set those multiples equal to 0
c) Solve for each angle in the trig fⁿs

Question 22

what to do if you find yourself stuck on an identity

Answer 22

look for conjugates. anywhere.

Question 23

how to get 1 from cot & csc

Answer 23

1 = csc² - cot²