Trigonometric equations

Question 1

What is 1 / sinx ?

Answer 1

cosec x

(cosectant)

Question 2

What is 1 / cos x?

Answer 2

sec x

(sectant)

Question 3

What is 1 / tanx?

Answer 3

cot x

cotangent

cos x / sin x

Question 4

Learn the graphs for:

y = cosec x

y = sec x

y = cot x

Answer 4

Do it

Question 5

Learn the trig identity relating sin²x and cos²x

Answer 5

sin²x + cos²x = 1

Question 6

Learn the trig identity relating tan²x and sec²x

Answer 6

tan²x + 1 = sec²x

Question 7

Learn the trig identity including cot²x and cosec²x?

Answer 7

1 + cot²x = cosec²x

Question 8

Why can the inverse of y = sin/cos/tan x not be found without restrictions of the domain?

Answer 8

All of them are not one-to-one mapping

Therefore must just take a section of the domain

Question 9

What are the restrictions that are taken of sin/cos/tan x for the graph of their inverse?

Answer 9

sinx: -90 <= x <= 90
cosx: 0 <= x <= 180
tanx: -90 <= x <= 90

Question 10

How do you find the inverse of a graph?

Answer 10

Refelct a graph in the line y=x

Question 11

Write the formula for sin(A+B)

Answer 11

sin(A+B) = sinAcosB + cosAsinB

Question 12

Write the formula for sin(A-B)

Answer 12

sinAcosB - cosAsinB

Question 13

Write the formula for cos(A+B)

Answer 13

cosAcosB - sinAsinB

Question 14

Write the formula for cos(A-B)

Answer 14

cosAcosB + sinAsinB

Question 15

Write the formula for tan(A+B)

Answer 15

tan(A+B) = (tanA + tan B) / (1 - tanAtanB)

Question 16

Write the formula for tan(A-B)

Answer 16

tan(A-B) = (tanA - tanB) / (1 + tanAtanB)

Question 17

Learn the double angle formula for sin2A

Answer 17

sin2A = 2sinAcosA

Question 18

Learn the double angle formulae for cos2A

Answer 18

cos2A = cos²A - sin²A

cos2A = 2cos²A - 1

cos2A = 1 - 2sin²A

Question 19

Learn the double angle formula for tan2A

Answer 19

tan2A = 2tanA / (1-tan²A)

Question 20

What do you do if the question asks you to write an equation in the form Rcos(2x+a)?

Answer 20

Expand to get R(cos2xcosa - sin2xsina)

(Rcosa)cos2x - (Rsina) sin2x

Then relate back to left hand side as things in the bracket must equal the constants on that left hand side

Calculate a using these values

Square (Rcosa) = constant from LHS and (Rsina) = constant from LHS

Add them together and use (sin²x + cos²x) to get R² = Sum of LHS constants²

Question 21

How do you convert sin²x/2 be converted to a form with just x?

Answer 21

Double angle formula, in this case x is double

cos x = 1 -2sin²x/2