1) Angles can be measured in degrees, minutes, or radians. Trigonometric functions relate to the sides of a right triangle and depend on the angle of rotation. 2) Positive angles are measured clockwise from the positive x-axis, negative angles counterclockwise. 3) The value of a trig function for any angle can be determined using a calculator, right triangles, or trig identities involving reference angles.

1. 1) Angles can be measured in degrees and minutes or in
TRIGONOMETRIC FUNCTIONS
TRIGONOMETRIC IDENTITIES
radians. ( π radian = 1800 )
How to determine the value of a 1) Complementary angles Identities
2) Positive angles are angle measured in the trigonometric function of any angle
anticlockwisesin2 A sin θ = cos(90 o − θ ) cot θ = tan(90 o − θ )
) sin2 A) direction from the positive x –axis. 1) By using Scientific Calculator
π 0
cos θ = sin(90 o − θ ) sec θ = cos ec(90 o − θ )
3) Negative angle are angle measured in the clockwise Eg: a) sin 350 (b) kos
direction from the positive x – axis 3 tan θ = cot(90 o − θ ) cos ecθ = sec(90 o − θ )
900
4) Quadrants Reference Angles 2) Without using calculators
2) Negative Angles Identities
II I a) By using right-angled triangle and a) Sin (- θ ) b) cos (- θ ) c) tan (- θ )
00 /
1800 3600 trigonometric ratio. = - sin θ = cos θ = - tan θ
III IV
270 0 Eg: Given cos θ = 3/5 and θ is
in quadrant 1. Find the value of 3) Basic identities
EXAMPLES sin θ , cosec θ , sec θ ,cot θ
5
a) sin2 A + cos2 A = 1
0 0 0
a) 45 b) - 70 c) 430 θ
θ 3
b) 1 + tan2 A = sec2 A
b) By using the value of the c) 1 + cot2 A = cosec2 A
trigonometric function of the reference
angle which is 10) Addition Formulae
i) a special angle
4) Six Trigonometric Functions Of Any Angles (00, 300, 600 , 900….) sin( A ± B ) = sin A cos B ± cos A sin B
r
ii) a given acute angle cos( A ± B) = cos A cos B  sin A sin B
y c) By using (a) or (b) and trigonometric tan A ± tan B
tan( A ± B ) =
θ identities. 1  tan A tan B
x
Special Angles 11) Double angle Half-angle formulae.
Sin θ = y / r cosec θ = 1 / sin θ Formulae 1 1
300 sin A = 2 sin A cos A
cos θ = x / r sec θ = 1 / cos θ 2 3 Sin 2A = 2 sin A cosA
2 2
tan θ = y / x cot θ = 1 / tan θ 1 1 1
600 450 cos A = cos2 A − sin2
Cos 2A =Cos2A - sin2A 2 2
1 1 1 1
5) The signs of the trigonometric functions. 2 = 1 – 2sin2 A
= 1 – 2 sin A 2
Sin θ + All positive 3O0 450 600 1
S+ A+ = 2 Cos2A - 1 = 2 cos2 A- 1
Cosec θ + Sin 2
2 tan A A
2 tan
tan θ + Cos θ + T+ C+ cos tan2A = 2 2
1 − tan A tan A =
Cot θ + Sec θ + A
tan 1 − tan 2
2