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Page 1 KEY POINTS ? A radian is an angle subtended at the centre of a circle by an arc whose length is equal to the radius of the circle. We denote 1 radian by 1 c . ? ? radian = 180 degree, 1° = 60’ 1 radian = 180 ? degree and 1’ = 60’ ’ 1 degree = 180 ? radian ? If an arc of length l makes an angle qradian at the centre of a circle of radius r, we have l r ? ? Page 2 KEY POINTS ? A radian is an angle subtended at the centre of a circle by an arc whose length is equal to the radius of the circle. We denote 1 radian by 1 c . ? ? radian = 180 degree, 1° = 60’ 1 radian = 180 ? degree and 1’ = 60’ ’ 1 degree = 180 ? radian ? If an arc of length l makes an angle qradian at the centre of a circle of radius r, we have l r ? ? Some Standard Results ? sin (x + y) = sinx cosy + cosx siny cos (x + y) = cosx cosy — sinx siny ta n ta n ta n(x + y) 1 ta n .ta n x y x y ? ? ? Page 3 KEY POINTS ? A radian is an angle subtended at the centre of a circle by an arc whose length is equal to the radius of the circle. We denote 1 radian by 1 c . ? ? radian = 180 degree, 1° = 60’ 1 radian = 180 ? degree and 1’ = 60’ ’ 1 degree = 180 ? radian ? If an arc of length l makes an angle qradian at the centre of a circle of radius r, we have l r ? ? Some Standard Results ? sin (x + y) = sinx cosy + cosx siny cos (x + y) = cosx cosy — sinx siny ta n ta n ta n(x + y) 1 ta n .ta n x y x y ? ? ? cot(x +y) = cot x.cot y1 coty + cotx ? sin (x — y) = sinx cosy — cosx siny cos (x — y) = cosx cosy + sinx siny ta n ta n ta n(x— y) 1 ta n .ta n x y x y ? ? ? cot .cot 1 cot(x— y) cot cot x y y x ? ? ? ? tan(x +y + z) = ta n ta n ta n ta n ta n ta n 1 ta n ta n ta n .ta n ta n ta n x y z x y z x y y z z x ? ? ? ? ? ? ? 2sinx cosy = sin(x + y) + sin(x — y) 2cosx siny = sin(x + y) — sin(x — y) 2cosx cosy = cos(x + y) + cos(x — y) 2sinx siny = cos(x — y) — cos(x + y) ? sin x + sin y = 2 sin 2 x y ? cos 2 x y ? sin x — sin y = 2 cos 2 x y ? sin 2 x y ? cos x +cos y = 2 cos 2 x y ? cos 2 x y ? cos x — cos y = — 2 sin 2 x y ? sin 2 x y ? 2sin s in 2 2 x y y x ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Page 4 KEY POINTS ? A radian is an angle subtended at the centre of a circle by an arc whose length is equal to the radius of the circle. We denote 1 radian by 1 c . ? ? radian = 180 degree, 1° = 60’ 1 radian = 180 ? degree and 1’ = 60’ ’ 1 degree = 180 ? radian ? If an arc of length l makes an angle qradian at the centre of a circle of radius r, we have l r ? ? Some Standard Results ? sin (x + y) = sinx cosy + cosx siny cos (x + y) = cosx cosy — sinx siny ta n ta n ta n(x + y) 1 ta n .ta n x y x y ? ? ? cot(x +y) = cot x.cot y1 coty + cotx ? sin (x — y) = sinx cosy — cosx siny cos (x — y) = cosx cosy + sinx siny ta n ta n ta n(x— y) 1 ta n .ta n x y x y ? ? ? cot .cot 1 cot(x— y) cot cot x y y x ? ? ? ? tan(x +y + z) = ta n ta n ta n ta n ta n ta n 1 ta n ta n ta n .ta n ta n ta n x y z x y z x y y z z x ? ? ? ? ? ? ? 2sinx cosy = sin(x + y) + sin(x — y) 2cosx siny = sin(x + y) — sin(x — y) 2cosx cosy = cos(x + y) + cos(x — y) 2sinx siny = cos(x — y) — cos(x + y) ? sin x + sin y = 2 sin 2 x y ? cos 2 x y ? sin x — sin y = 2 cos 2 x y ? sin 2 x y ? cos x +cos y = 2 cos 2 x y ? cos 2 x y ? cos x — cos y = — 2 sin 2 x y ? sin 2 x y ? 2sin s in 2 2 x y y x ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? sin 2x = 2 sin x cos x = 2 2 tan 1 tan x x ? ? cos 2x = cos 2 x — sin 2 x = 2 cos 2 x — 1 = 1 — 2sin 2 x = 2 2 1 ta n 1 ta n x x ? ? ? tan 2x = 2 2 tan 1 tan x x ? ? sin 3x = 3 sinx — 4 sin 3 x ? cos 3x = 4 cos 3 x — 3 cos x ? tan 3x = 3 2 3ta n ta n 1 3ta n x x x ? ? ? sin(x + y) sin(x — y) = sin 2 x — sin 2 y= cos 2 y — cos 2 x ? cos(x + y) cos(x — y) = cos 2 x — sin 2 y= cos 2 y — sin 2 x ? General solution — A solution of a trigonometric equation, generalised by means of periodicity, is known as the general solution. ? Principal solutions — The solutions of a trigonometric equation which lie in [0,2 ?) are called its principal solutions. ? sin ? = 0 ? ? ?? = n ? ? ? where ? n ? ? z ? cos ? = 0 ? ? ? ? = (2n ? ? ? 2 ? , where n ? ? z ? tan ? = 0 ? ? ?? = n ? ? ? where ? n ? ? z ? sin ? = sin ? ? ? ? ? = n ? ? ?(— 1) n ? ? where n ? z ? cos ? = cos ? ? ? ? ?? = 2n ? ? ? ? ? ? where n ? ? z ? tan ? = tan ? ? ? ? ?? = n ? ? ? ? ? ? where n ? ? z Page 5 KEY POINTS ? A radian is an angle subtended at the centre of a circle by an arc whose length is equal to the radius of the circle. We denote 1 radian by 1 c . ? ? radian = 180 degree, 1° = 60’ 1 radian = 180 ? degree and 1’ = 60’ ’ 1 degree = 180 ? radian ? If an arc of length l makes an angle qradian at the centre of a circle of radius r, we have l r ? ? Some Standard Results ? sin (x + y) = sinx cosy + cosx siny cos (x + y) = cosx cosy — sinx siny ta n ta n ta n(x + y) 1 ta n .ta n x y x y ? ? ? cot(x +y) = cot x.cot y1 coty + cotx ? sin (x — y) = sinx cosy — cosx siny cos (x — y) = cosx cosy + sinx siny ta n ta n ta n(x— y) 1 ta n .ta n x y x y ? ? ? cot .cot 1 cot(x— y) cot cot x y y x ? ? ? ? tan(x +y + z) = ta n ta n ta n ta n ta n ta n 1 ta n ta n ta n .ta n ta n ta n x y z x y z x y y z z x ? ? ? ? ? ? ? 2sinx cosy = sin(x + y) + sin(x — y) 2cosx siny = sin(x + y) — sin(x — y) 2cosx cosy = cos(x + y) + cos(x — y) 2sinx siny = cos(x — y) — cos(x + y) ? sin x + sin y = 2 sin 2 x y ? cos 2 x y ? sin x — sin y = 2 cos 2 x y ? sin 2 x y ? cos x +cos y = 2 cos 2 x y ? cos 2 x y ? cos x — cos y = — 2 sin 2 x y ? sin 2 x y ? 2sin s in 2 2 x y y x ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? sin 2x = 2 sin x cos x = 2 2 tan 1 tan x x ? ? cos 2x = cos 2 x — sin 2 x = 2 cos 2 x — 1 = 1 — 2sin 2 x = 2 2 1 ta n 1 ta n x x ? ? ? tan 2x = 2 2 tan 1 tan x x ? ? sin 3x = 3 sinx — 4 sin 3 x ? cos 3x = 4 cos 3 x — 3 cos x ? tan 3x = 3 2 3ta n ta n 1 3ta n x x x ? ? ? sin(x + y) sin(x — y) = sin 2 x — sin 2 y= cos 2 y — cos 2 x ? cos(x + y) cos(x — y) = cos 2 x — sin 2 y= cos 2 y — sin 2 x ? General solution — A solution of a trigonometric equation, generalised by means of periodicity, is known as the general solution. ? Principal solutions — The solutions of a trigonometric equation which lie in [0,2 ?) are called its principal solutions. ? sin ? = 0 ? ? ?? = n ? ? ? where ? n ? ? z ? cos ? = 0 ? ? ? ? = (2n ? ? ? 2 ? , where n ? ? z ? tan ? = 0 ? ? ?? = n ? ? ? where ? n ? ? z ? sin ? = sin ? ? ? ? ? = n ? ? ?(— 1) n ? ? where n ? z ? cos ? = cos ? ? ? ? ?? = 2n ? ? ? ? ? ? where n ? ? z ? tan ? = tan ? ? ? ? ?? = n ? ? ? ? ? ? where n ? ? z 5 1 sin18 4 ? ? ? ; 10 2 5 cos18 4 ? ? ? 10 2 5 5 1 sin36 ; cos36 4 4 ? ? ? ? ? ?Read More
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1. What are the main trigonometric functions? 
2. How are trigonometric functions used in reallife applications? 
3. What is the unit circle and its relationship with trigonometric functions? 
4. How are trigonometric functions related to rightangled triangles? 
5. How can trigonometric functions be used to solve problems involving angles and sides in triangles? 
209 videos443 docs143 tests


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