Additional Mathematics: Trigonometry

angles in quadrants (anticlockwise)

all, sin, tangent, cosine

when measuring angles in quadrants we measure from the

horizontal lines

sin 30

cos 30

tan 30

sin 150

cos 330

tan 210

how to find negative related quadrants

find the angle in the positive quadrants, find the quadrants the angle would be negative in and plot it, follow the same procedure

if they give you the negative angle and ask you to to find the positive, find the angle it makes with the horizontal line and put it in the positive quadrants

rule about equivalent angles in negative quadrants

if there is a trigonometrical angle in a quadrant where that trig ratio is negative, then the related angle will be negative (e.g sin 240 exists in the tangent quadrant, where sin is negtiave, so its equivalent angle would be -sin 80)

sin 60

√3/2

cos 30

√3/2

sin 30

½

cos 60

½

tan 60

√3

tan 30

1/√3

tan 45

1

cos 45

1/√2

sin 45

1/√2

equal sin and cosine angles

cos 45 = sin 45

cos 30 = sin 60

cos 60 = sin 30

rule for sin and cos angles

sin θ = 90 - cos θ

cos² θ + sin² θ

1

sin² θ

1 - cos² θ

cos² θ

1 - sin² θ

tan θ

sin θ/cos θ

sec θ

1/cos θ

cot θ

cos θ/sin θ

cos (A + B)

cosAcosB - sinAsinB

cos (A-B)

cosAcosB + sinAsinB

sin (A+B)

sinAcosB +sinBcosA

sin (A-B)

sinAcosB - sinBcosA

tan (A+B)

tan A + tan B / 1-tanAtanB

AND

sin (A+B)/cos (A+B)

tan (A-B)

tan A - tan B / 1 + tanAtanB

AND

sin (A-B)/cos (A-B)

sin 2A

2sinAcosA

cos 2A

cos² A - sin² A

AND

2cos² A - 1

AND

1 - sin² A

sin 2A

2tan A / 1 - tan² A

triangular method of solving trigs

from the trigonometrical values they give you, draw a triangle. find the missing side using the pythagoras theorem, then insert the different tan, sin and cos values into your questions

how to convert cos, tan and sin values to pi

divide angle by 180 and multiply by π

sin 90 (π/2)

1

sin 180 (π)

0

sin 270 (3/2π)

-1

sin 360 (2π)

0

cos 90 (π/2)

0

cos 180 (π)

-1

cos 270 (3/2π)

0

cos 360 (2π)

1

tan 90 (π/2)

∞

tan 180 (π)

0

tan 270 (3/2π)

∞

tan 360 (2π)

0

how to work with the inverse of angles 0, 1, -1, and ∞

sin^-1 would be equal to all of the sin angles result in 1.

for example:
sin^-1 = sin 90, because sin 90 = 1

use the regular sin (angle) = number, the sin inverse of the number is equal to the angle