RESOU PAGES MATHEMATICS y x x 1 x y x2 0 b y1 y2 x y r θ 1 45˚ 45˚ 1 2 1 60˚ 30˚ 2 3 a c b B r r r y x θ Equation of a straight line y – y 1 = m(x – x 1 ) where m = slope = rise run = y = y 2 – y 1 x x2 – x 1 or y = mx + b where m = slope, b = y-intercept sin = y (opposite/hypotenuse) =1/ csc r cos = x (adjacent/hypotenuse) =1/ sec r tan = y (opposite/adjacent) =1/ cot x tan = 1+cot2 = csc2 sin2 +cos2 = 1 cos 2 –sin2 = cos2 1+tan2 = sec2 sec = 1 sin 45° = 1 cos 45° = = 1 = tan 45° = 1 2 2 2 2 3 3 2 2 sin (A+B) = sin A cos B + cos A sin B sin (A–B) = sin A cos B – cos A sin B tan (A+B) = tan A+ tan B 1– tan A tan B tan (A–B) = tan A – tan B 1 + tan A tan B cos (A+B) = cos A cos B – sin A sin B cos (A–B) = cos A cos B + sin A sin B Quad II Quad I sin+ all ratios+ Quad III Quad IV tan+ cos+ *undefined for and = 1 radian 2π radians = 360° 0 π/2 π/2 π 3π/2 3π/2 2π sin 0 1 0 –1 0 cos 1 0 * –1 0 1 tan 0 0 0 a = b = c sinA sinB sinC a2 = b2+ c2– 2bc cos A b2 = a2+ c2– 2ac cos B c2 = a2+ b2– 2ab cos C y = sin(x) y = cos(x) y = tan(x) sin 30° = 1 cos 30° = 3 tan 30° = 1 = 2 2 3 sin 60° = 3 cos 60° = 1 tan 60° = 3 2 2 cot = cos cos sin sin A C cos * y x -360° -270° -180° -90° 0 90° 180° 270° 360° -2 - 2 1 1 2 -1 2 -1 RESOU PAGES AT EMATICS y x x 1 x y x2 0 b y1 y2 x y r θ 1 45˚ 45˚ 1 2 1 60˚ 30˚ 2 3 a c b B r r r y x θ Equation of a straight line y – y 1 = m(x – x 1 ) where m = slope = rise run = y = y 2 – y 1 x x2 – x 1 or y = mx + b where m = slope, b = y-intercept sin = y (opposite/hypotenuse) =1/ csc r cos = x (adjacent/hypotenuse) =1/ sec r tan = y (opposite/adjacent) =1/ cot x tan = 1+cot2 = csc2 sin2 +cos2 = 1 cos 2 –sin2 = cos2 1+tan2 = sec2 sec = 1 sin 45° = 1 cos 45° = = 1 = tan 45° = 1 2 2 2 2 3 3 2 2 sin (A+B) = sin A cos B + cos A sin B sin (A–B) = sin A cos B – cos A sin B tan (A+B) = tan A+ tan B 1– tan A tan B tan (A–B) = tan A – tan B 1 + tan A tan B cos (A+B) = cos A cos B – sin A sin B cos (A–B) = cos A cos B + sin A sin B Quad II Quad I sin+ all ratios+ Quad III Quad IV tan+ cos+ *undefined for and = 1 radian 2π radians = 360° 0 π/2 π/2 π 3π/2 3π/2 2π sin 0 1 0 –1 0 cos 1 0 * –1 0 1 tan 0 0 0 a = b = c sinA sinB sinC a2 = b2+ c2– 2bc cos A b2 = a2+ c2– 2ac cos B c2 = a2+ b2– 2ab cos C y = sin(x) y = cos(x) y = tan(x) sin 30° = 1 cos 30° = 3 tan 30° = 1 = 2 2 3 sin 60° = 3 cos 60° = 1 tan 60° = 3 2 2 cot = cos cos sin sin A C cos * y x -360° -270° -180° -90° 0 90° 180° 270° 360° -2 - 2 1 1 2 -1 2 -1 RES PAG MATHEMATICS y x x 1 x y x2 0 b y1 y2 x y r θ 1 45˚ 45˚ 1 2 1 60˚ 30˚ 2 3 a c b B r r r y x θ Equation of a straight line y – y 1 = m(x – x 1 ) where m = slope = rise run = y = y 2 – y 1 x x2 – x 1 or y = mx + b where m = slope, b = y-intercept sin = y (opposite/hypotenuse) =1/ csc r cos = x (adjacent/hypotenuse) =1/ sec r tan = y (opposite/adjacent) =1/ cot x tan = 1+cot2 = csc2 sin2 +cos2 = 1 cos 2 –sin2 = cos2 1+tan2 = sec2 sec = 1 sin 45° = 1 cos 45° = = 1 = tan 45° = 1 2 2 2 2 3 3 2 2 sin (A+B) = sin A cos B + cos A sin B sin (A–B) = sin A cos B – cos A sin B tan (A+B) = tan A+ tan B 1– tan A tan B tan (A–B) = tan A – tan B 1 + tan A tan B cos (A+B) = cos A cos B – sin A sin B cos (A–B) = cos A cos B + sin A sin B Quad II Quad I sin+ all ratios+ Quad III Quad IV tan+ c s+ *undefined for and = 1 radian 2π radians = 360° 0 π/2 π/2 π 3π/2 3π/2 2π sin 0 1 0 –1 0 cos 1 0 * –1 0 1 tan 0 0 0 a = b = c sinA sinB sinC a2 = b2+ c2– 2bc cos A b2 = a2+ c2– 2ac cos B c2 = a2+ b2– 2ab cos C y = sin(x) y = cos(x) y = tan(x) sin 30° = 1 cos 30° = 3 tan 30° = 1 = 2 2 3 sin 60° = 3 cos 60° = 1 tan 60° = 3 2 2 cot = cos cos sin sin A C cos * y x -360° -270° -180° -90° 0 90° 180° 270° 360° -2 - 2 1 1 2 -1 2 -1 RESOU PAGES MATHEMATICS y x x 1 x y x2 0 b y1 y2 x y r θ 1 45˚ 45˚ 1 2 1 60˚ 30˚ 2 3 a c b B r r r y x θ Equation of a straight line y – y 1 = m(x – x 1 ) where = slope = rise run = y = y 2 – y 1 x x2 – x 1 or y = mx + b where m = slope, b = y-intercept sin = y (opposite/hypotenuse) =1/ csc r cos = x (adjacent/hypotenuse) =1/ sec r tan = y (opposite/adjacent) =1/ cot x tan = 1+ t2 = csc2 si 2 + o 2 1 cos 2 –sin2 = cos2 1+tan2 = sec2 sec = 1 sin 45° = 1 cos 45° = = 1 = tan 45° = 1 2 2 3 2 sin (A+B) = sin A cos B + cos A sin B si ( – ) i os B – c s si tan (A+B) = tan A+ tan B 1– tan A tan B tan (A–B) = tan A – tan B 1 + tan A t B cos (A+B) = cos A cos B – sin A sin B s ( – ) + i i Quad II Quad I sin+ all ratios+ Quad III Quad IV tan+ cos+ *undefined for and = 1 radian 2π radians = 360° 0 π/2 π/2 π 3π/2 3π/2 2π sin 1 0 –1 0 cos 1 0 * –1 0 1 tan 0 0 0 a = b = c sinA sinB sinC a2 = b2+ c2– 2bc cos A b2 a + 2 a c B c = b2 b c s C y = sin(x) y = cos(x) y = tan(x) sin 30° = 1 cos 30° = 3 tan 30° = 1 = 2 2 3 sin 60° = 3 cos 60° = 1 tan 60° = 3 2 2 cot = cos cos sin A C cos * y x -360° -270° -180° -90° 0 90° 180° 270° 360° -2 - 2 1 1 2 -1 2 -1 RESOU MATHE I S y x x 1 x y x2 0 y1 y2 x y r θ 1 45˚ 45˚ 1 2 1 60˚ 30˚ 2 3 a c b r r r y x θ Equation f str i t li y 1 m( – 1 ) wher sl ise run y 2 – 1 x2 – x 1 or w r sl , -i t r t sin = y ( sit / t s ) / csc c s x ( j t/hypote use) 1/ sec r tan = (opposite/adjacent) = / cot x t c t2 csc2 sin2 +cos2 = 1 c s 2 si 2 = cos2 1+tan2 sec2 sec = 1 si ° 1 cos 45° = 1 = tan 45° = 1 2 2 2 3 2 + ) i c + s si sin ( ) sin A cos c s si t ( ) tan A+ tan B t t B t n (A–B) t A t t t c ) i i c s ( ) = cos A cos B + sin A si Q II I sin+ ll r ti s+ Quad III I t c s *undefined for = 1 radian 2π radians = ° 0 π/ π/2 π 3π/ 3π/ si 1 0 1 cos 1 0 * –1 0 1 t 0 = = c si sinB si a2 = 2 2 c b2 = 2 c c c s B c2 2 2 c s C i ( ) ( ) t ( ) sin 30° = cos 30° tan 30° = = 2 3 sin 60° = c s ° ta ° cot cos cos sin sin A C cos * y x -360° -270° -180° -90° ° 180° ° ° - - 1 2 -1 2 -1 RESOU PAGES MATHEMATICS y x x 1 x y x2 0 b y1 y2 x y r θ 1 45˚ 45˚ 1 2 1 60˚ 30˚ 2 3 a c b B r r r y x θ Equation of a straight line y – y 1 = m(x – x 1 ) where m = slope = rise run = y = y 2 – y 1 x x2 – x 1 or y = mx + b where m = slope, b = y-intercept sin = y (opposite/hypotenuse) / csc r cos = x (adjacent/hypotenuse) =1/ sec r tan = y (opposite/adjacent) =1/ cot x tan = 1+cot2 = csc2 sin2 +cos2 = 1 cos 2 –sin2 = cos 1+tan2 = sec2 sec = 1 sin ° cos ° 1 = tan 45° = 1 2 2 2 3 3 sin (A+B) = sin A cos B + cos A sin B sin (A–B) = sin A cos B – cos A sin B tan (A+B) = an + t – t ta tan (A–B) = tan A – tan B 1 + tan A tan B cos (A+B) = cos A cos B – sin A sin B cos (A–B) = cos A cos B + sin A sin B Quad II ua I si all ratios+ Quad III Quad IV tan+ cos+ *undefined for and = 1 radian 2π radians = 360° π/2 π/2 π 3π/2 3π/2 2π sin 0 1 0 –1 0 cos 1 0 * –1 0 1 tan 0 0 0 a = b = c sinA sinB sinC a2 = b2+ c2– 2bc cos A b2 = a2+ c2– 2ac cos B c2 = a2+ b2– 2ab cos C y = sin(x) y = cos(x) y = tan(x) sin ° 1 cos ° 3 tan 30° = 1 = 2 3 sin 60° 3 cos 60° = 1 tan 60° = 3 2 cot = o cos sin sin A C cos * y x -360° -270° -180° -90° 0 90° 180° 270° 360° -2 - 2 1 1 2 -1 2 -1 RESOURCE PAGES EMATICS y x x 1 x y x2 0 b y1 y2 x y r θ 45˚ 1 2 1 60˚ 30˚ 2 3 a c b B r r r y x θ on of a straight line m(x – x 1 ) m = slope = rise run = y = y 2 – y 1 x x2 – x 1 or y = mx + b where m = slope, b = y-intercept y (opposite/hyp tenu e) =1/ csc r x (adjacent/hypotenuse) =1/ sec r y (opposite/adjacent) =1/ cot x tan = 1+cot2 = csc2 sin2 +cos2 = 1 cos 2 –sin2 = cos2 1+tan2 = sec2 c = 1 sin 45° = 1 cos 45° = = 1 = tan 45° = 1 2 2 2 2 3 3 2 2 +B) = sin A cos B + co A sin B –B) = sin A cos B – cos A sin B tan (A+B) = tan A+ tan B 1– tan A tan B tan (A–B) = tan A – tan B 1 + tan A tan B cos (A+B) = cos A cos B – sin A sin B cos (A–B) = cos A cos B + sin A in B Quad II sin+ all r tios+ Quad III uad IV tan+ cos *undefined for and = 1 radian 2π radians = 360° 0 π/2 π/2 π 3π/2 3π/2 2π sin 0 1 0 –1 0 cos 1 0 * –1 0 1 tan 0 0 0 a = b = c sinA sinB sinC a2 = b2+ c2– 2bc cos A b2 = a2+ c2– 2ac cos B c2 = a2+ b2– 2ab cos C in(x) y = co (x) y = tan(x) sin 30° = 1 cos 30° = 3 tan 30° = 1 = 2 2 3 sin 60° = 3 cos 60° = 1 tan 60° = 3 2 2 cot = cos cos sin sin A C cos * y x -360° -270° -180° -90° 0 90° 180° 270° 360° -2 - 2 1 1 2 -1 2 -1 RESOU PAGES MATHEMATICS y x x 1 x y x2 0 b y1 y2 x y r θ 1 45˚ 45˚ 1 2 1 60˚ 30˚ 2 3 a c b B r r r y x θ Equation of a straight line y – y 1 = m(x – x 1 ) where m = slope = rise run = y = y 2 – y 1 x x2 – x 1 or y = mx + b where m = slope, b = y-intercept sin = y (opposite/hypotenuse) =1/ csc r cos = x (adjacent/hypotenuse) =1/ sec r tan = y (opposite/adjacent) =1/ cot x tan = 1+cot2 = csc2 sin2 +cos2 = 1 cos 2 –sin2 = cos2 1+tan2 = sec2 sec = 1 sin 45° = 1 cos 45° = = 1 = ta ° 1 2 2 2 3 3 2 2 sin (A+B) = sin A cos B + cos A sin B sin (A–B) = sin A cos B – cos A sin B tan (A+B) = tan A+ tan B 1– tan A tan B tan (A–B) = tan A – tan B 1 + tan A ta cos (A+B) = cos A cos B – sin A sin B cos (A–B) = cos A cos B + sin A sin B Quad II Quad I sin+ all ratios+ Quad III Quad IV tan+ cos+ *undefi ed for and = 1 radian 2π radians = 360° 0 π/2 π/2 π 3π/2 3π/2 2π sin 0 1 0 –1 0 cos 1 0 * –1 0 1 tan 0 0 0 a = b = c sinA sinB sinC a2 = b2+ c2– 2bc cos A b2 = a2+ c2– 2ac cos B c2 = a2+ b2– ab cos C y = sin(x) y = cos(x) y = tan(x) sin 30° = 1 cos 30° = 3 tan 30° = 1 = 2 2 3 sin 60° = 3 cos 60° = 1 tan 60° 2 2 cot = cos co sin sin A C cos * y x -360° -270° -180° -90° 0 90° 180° 270° 360° -2 - 2 1 1 2 -2 -1 RESOU PAGES AT E ATICS y x x 1 x y x2 0 b y1 y2 x y r θ 1 45˚ 45˚ 1 2 1 60˚ ˚ 2 3 a c b B r r r y x θ Equation of a straight line y – y 1 = m(x – x 1 ) where m = slope = rise run = y = y 2 – y 1 x x2 – x 1 or y = mx + b where = slope, b = y-intercept sin = y (opposite/hypotenuse) =1/ csc r cos = x (adjacent/hypotenuse) =1/ sec r tan = y (opposite/adjacent) =1/ cot x tan = 1+cot2 = csc2 sin2 +cos2 = 1 cos 2 –sin2 = cos2 1+tan2 = sec2 sec = 1 sin 45° = 1 cos 45° = = 1 = tan 45° = 1 2 2 2 2 3 3 2 2 sin (A+B) = sin A cos B + cos A sin B sin (A–B) = sin A cos B – cos A sin B tan (A+B) = tan A+ tan B 1– tan A tan B tan (A–B) = t A – tan B 1 + tan A tan B cos (A+B) = cos A cos B – sin A sin B cos (A–B) = cos A cos B + sin A sin B Quad II Qu d I sin+ all ratios+ Qu d III Quad IV tan+ cos+ *undefined for and = 1 radian 2π radians = 360° 0 π/2 π/2 π 3π/2 3π/2 2π sin 0 1 0 –1 0 cos 1 0 * –1 0 1 ta 0 0 0 a = b = c sinA sinB sinC a2 = b2+ c2– 2bc cos A b2 = a2+ c2– 2ac cos B c2 = a2+ b2– 2ab cos C y = sin(x) y = cos(x) y = tan(x) sin 30° = 1 cos 30° = 3 ta 30° = 1 = 2 2 3 sin 60° = 3 cos 60° = 1 tan 60° = 3 2 2 cot = cos cos sin sin A C cos * y x -360° -270° -180° -90° 0 90° 180° 270° 360° -2 - 2 1 1 2 -1 2 -1 Linear Trigonometry TRIGONOMETRIC RATIOS C A S T Value of trig ratio SINE LAW COSINE LAW R–12 RESOURCE PAGES
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