Trigonometric identities and equations

Question 1

for point P(x,y) on a unit circle such that OP makes an angle θ with the positive x axis anticlockwise

Answer 1

• cosθ = x coord
• sinθ = y coord
• tanθ = y/x, gradient of OP

Question 2

which trigonometric ratios are positive in which quadrants

Answer 2

tan | cos

Question 3

rules to find acute sin angles made with the x axis

Answer 3

sin(180°-θ) = sinθ
sin(180°-θ) = -sinθ
sin(360°-θ) = -sinθ

Question 4

rules to find acute cos angles made with the x axis

Answer 4

cos(180°-θ) = -cosθ
cos(180°+θ) = -cosθ
cos(360°-θ) = cosθ

Question 5

rules to find acute tan angles made with the x axis

Answer 5

tan(180°-θ) = -tanθ
tan(180°+θ) = tanθ
tan(360°-θ) = -tanθ

Question 6

formula connecting sin² and cos²

Answer 6

sin²θ + cos²θ = 1

Question 7

formula for tan

Answer 7

tanθ = sinθ ÷ cosθ

Question 8

range for k when sin/cos/tanθ = k

Answer 8

for sinθ and cosθ, -1≤k≤1

for tanθ, k can be all values

Question 9

what is the angle called when used the inverse trigonometric function

Answer 9

principal value

Question 10

what ranges will a calculator give for principal values

Answer 10

cos-¹ 0≤θ≤180°

sin-¹ -90°≤θ≤90°

tan-¹ -90°≤θ≤90°