Chapter 10 - Trig identities and equations

Question 1

All trig ratios are positive in what quadrant?

Answer 1

First quadrant

Question 2

What quadrants is sin x positive?

Answer 2

1st and 2nd quadrant (from 0^o to 180⁰)

Question 3

In what quadrants is cos x positive?

Answer 3

1st and 4th quadrants (0⁰ to 90⁰ and 270⁰ to 360^o)

Question 4

In what quadrants is tan x positive?

Answer 4

1st and 3rd quadrants (0^o to 90⁰, and 180^o to 270⁰)

Question 5

How do you find all solutions to a trig equation eg. sin x = 1/2 ?

Answer 5

1. Find the angle = sin^-1 (1/2) in the 1 st quadrant (30^o)
2. Draw CAST diagram and draw on 2 diagonal lines showing 4 different 30^o angle with horizontal axis
3. identify quadrants where sin x is positive (or negative if asked to solve sin x = -1/2)
4. Work out angles in those quadrants, measuring angle from 0^o in anti-clockwise direction. ie 30^o and 180-30 = 150^o

Question 6

What is value of sin 30?

Answer 6

1/2

Question 7

What is value of cos 30?

Answer 7

sq root (3) / 2

Question 8

What is the value of tan 30?

Answer 8

sq root (3) / 3

Question 9

What is the value of sin 45?

Answer 9

sq root (2) / 2

Question 10

What is the value of cos 45?

Answer 10

sq root (2) / 2

Question 11

What is the value of tan 45?

Answer 11

1

Question 12

sin²x + cos²x = ?

Answer 12

1

Question 13

What is the equation linking sin²x and cos²x?

Answer 13

sin²x + cos²x = 1

Question 14

What is the equation linking sin x, cos x and tan x?

Answer 14

tan x = sin x

cos x