Sin theta formula

Trigonometric Identities Email this page to a friend Resources · · · · · · Search Trigonometric Identities ( sin(theta) = a / c csc(theta) = 1 / sin(theta) = c / a cos(theta) = b / c sec(theta) = 1 / cos(theta) = c / b tan(theta) = sin(theta) / cos(theta) = a / b cot(theta) = 1/ tan(theta) = b / a sin(-x) = -sin(x) csc(-x) = -csc(x) cos(-x) = cos(x) sec(-x) = sec(x) tan(-x) = -tan(x) cot(-x) = -cot(x) sin ^2(x) + cos ^2(x) = 1 tan ^2(x) + 1 = sec ^2(x) cot ^2(x) + 1 = csc ^2(x) sin(x y) = sin x cos y cos x sin y cos(x y) = cos x cosy sin x sin y tan(x y) = (tan x tan y) / (1 tan x tan y) sin(2x) = 2 sin x cos x cos(2x) = cos ^2(x) - sin ^2(x) = 2 cos ^2(x) - 1 = 1 - 2 sin ^2(x) tan(2x) = 2 tan(x) / (1 - tan ^2(x)) sin ^2(x) = 1/2 - 1/2 cos(2x) cos ^2(x) = 1/2 + 1/2 cos(2x) sin x - sin y = 2 sin( (x - y)/2 ) cos( (x + y)/2 ) cos x - cos y = -2 sin( (x - y)/2 ) sin( (x + y)/2 ) Trig Table of Common Angles angle 0 30 45 60 90 sin ^2(a) 0/4 1/4 2/4 3/4 4/4 cos ^2(a) 4/4 3/4 2/4 1/4 0/4 tan ^2(a) 0/4 1/3 2/2 3/1 4/0 Given Triangle abc, with angles A,B,C; a is opposite to A, b opposite B, c opposite C: a/sin(A) = b/sin(B) = c/sin(C) (Law of Sines) c ^2 = a ^2 + b ^2 - 2ab cos(C) b ^2 = a ^2 + c ^2 - 2ac cos(B) a ^2 = b ^2 + c ^2 - 2bc cos(A) (Law of Cosines) (a - b)/(a + b) = tan [(A-B)/2] / tan [(A+B)/2] (Law of Tangents) Contact us | Advertising & Sponsorship | Partnership | Link to us © 2000-2005 Math.com. All rights reserved.

Sin Theta Formula Apart from cos and tan, the sine function is an essential trigonometric function. The ratio of the opposite side and the hypotenuse is known as sine theta. Consider the below right-angled triangle ABC, Sin θ = opposite side/hypotenuse = CB/AC If theta is shifted to C from A, then the formula would transform as below Sin θ = opposite side/hypotenuse = AB/AC SIN θ Values The below table shows the values of sin θ for various degrees Sin θ degree value 0 0 30 ½ 45 1√ 2 60 3√ 2 90 1 180 0 Sine Wave The below graph shows how sine wave looks like If we look into calculus the differentiation of sin θ = cos θ whereas on integrating we get – cos θ More Sin Theta Formula • Sin (- D) = – sin D • Sin (90 – R) = cos R • Sin (180 – B) = sin B • sin 2 M + cos 2 M = 1 • A+B =Sin A ×Cos B+Cos A ×Sin B • A-B =Sin A ×Cos B-Cos A ×Sin B • Sin 2 θ = 2 sin θ. cos θ • Sin 3 θ = 3 sin θ – 4 sin 3 θ Solved Examples 1. If cos θ = 24/25 then find the value of sin θ using sin theta formula. We know that, sin² θ + cos² θ = 1 Sin² θ=1- cos² 2. On a building site, John was working. He’s trying to get to the top of the wall. A 44-foot ladder connects the top of the wall to a location on the ground. The ladder forms a 60-degree angle with the ground. What would the wall’s height be? We know that sin 60 = √3/2, also sin θ here in this case would be wall’s height/ladder 3. In a 7,24,25 right angled triangle at B. what would be the value of Sin C ? Sin C = Opposite side/hypotenuse = AB/AC =2...

You would need an expression to work with. For example: Given #sinalpha=3/5# and #cosalpha=-4/5#, you could find #sin2 alpha# by using the double angle identity #sin2 alpha=2sin alpha cos alpha#. #sin2 alpha=2(3/5)(-4/5)=-24/25#. You could find #cos2 alpha# by using any of: #cos2 alpha=cos^2 alpha -sin^2 alpha# #cos2 alpha=1 -2sin^2 alpha# #cos2 alpha=2cos^2 alpha -1# In any case, you get #cos alpha=7/25#.

The term Trigonometry is derived from Greek words i.e; trigonon and metron, which implies triangle and to measure respectively, θ. There are 6 Trigonometry ratios namely, Sine, Cosine, Tangent, Cotangent, Secant, and Cosecant. These trigonometry ratios tell the different combinations in a right-angled triangle. Trigonometric ratios Trigonometric ratios are ratios of the lengths of the right-angled triangle. These ratios can be used to determine the ratios of any two sides out of a total of three sides of a right-angled triangle. • Sine function: The sine ratio for the given angle θ in a right-angled triangle is defined as the ratio of lengths of its opposite side to its hypotenuse. i.e., Sinθ = AB/AC • Cosine function: The Cosine ratio for the given angle θ in a right-angled triangle is defined as the ratio of lengths of its adjacent side to its hypotenuse. i.e, Cosθ = BC/AC • Tangent Function: The Tangent ratio for the given angle θ in a right-angled triangle is defined as the ratio of lengths of its opposite side to its adjacent. i.e, Tanθ = AB/BC • Cotangent Function: The Cotangent ratio for the given angle θ in a right-angled triangle is defined as the ratio of lengths of its adjacent side to its opposite. It’s the reciprocal of the tan ratio. i.e, Cotθ = BC/AB =1/Tanθ • Secant Function: The Secant ratio for the given angle θ in a right-angled triangle is defined as the ratio of lengths of its Hypotenuse side to its adjacent. i.e, Secθ = AC/BC • Cosecant Function: The ...

You would need an expression to work with. For example: Given #sinalpha=3/5# and #cosalpha=-4/5#, you could find #sin2 alpha# by using the double angle identity #sin2 alpha=2sin alpha cos alpha#. #sin2 alpha=2(3/5)(-4/5)=-24/25#. You could find #cos2 alpha# by using any of: #cos2 alpha=cos^2 alpha -sin^2 alpha# #cos2 alpha=1 -2sin^2 alpha# #cos2 alpha=2cos^2 alpha -1# In any case, you get #cos alpha=7/25#.

Sin Theta Formula Apart from cos and tan, the sine function is an essential trigonometric function. The ratio of the opposite side and the hypotenuse is known as sine theta. Consider the below right-angled triangle ABC, Sin θ = opposite side/hypotenuse = CB/AC If theta is shifted to C from A, then the formula would transform as below Sin θ = opposite side/hypotenuse = AB/AC SIN θ Values The below table shows the values of sin θ for various degrees Sin θ degree value 0 0 30 ½ 45 1√ 2 60 3√ 2 90 1 180 0 Sine Wave The below graph shows how sine wave looks like If we look into calculus the differentiation of sin θ = cos θ whereas on integrating we get – cos θ More Sin Theta Formula • Sin (- D) = – sin D • Sin (90 – R) = cos R • Sin (180 – B) = sin B • sin 2 M + cos 2 M = 1 • A+B =Sin A ×Cos B+Cos A ×Sin B • A-B =Sin A ×Cos B-Cos A ×Sin B • Sin 2 θ = 2 sin θ. cos θ • Sin 3 θ = 3 sin θ – 4 sin 3 θ Solved Examples 1. If cos θ = 24/25 then find the value of sin θ using sin theta formula. We know that, sin² θ + cos² θ = 1 Sin² θ=1- cos² 2. On a building site, John was working. He’s trying to get to the top of the wall. A 44-foot ladder connects the top of the wall to a location on the ground. The ladder forms a 60-degree angle with the ground. What would the wall’s height be? We know that sin 60 = √3/2, also sin θ here in this case would be wall’s height/ladder 3. In a 7,24,25 right angled triangle at B. what would be the value of Sin C ? Sin C = Opposite side/hypotenuse = AB/AC =2...

The term Trigonometry is derived from Greek words i.e; trigonon and metron, which implies triangle and to measure respectively, θ. There are 6 Trigonometry ratios namely, Sine, Cosine, Tangent, Cotangent, Secant, and Cosecant. These trigonometry ratios tell the different combinations in a right-angled triangle. Trigonometric ratios Trigonometric ratios are ratios of the lengths of the right-angled triangle. These ratios can be used to determine the ratios of any two sides out of a total of three sides of a right-angled triangle. • Sine function: The sine ratio for the given angle θ in a right-angled triangle is defined as the ratio of lengths of its opposite side to its hypotenuse. i.e., Sinθ = AB/AC • Cosine function: The Cosine ratio for the given angle θ in a right-angled triangle is defined as the ratio of lengths of its adjacent side to its hypotenuse. i.e, Cosθ = BC/AC • Tangent Function: The Tangent ratio for the given angle θ in a right-angled triangle is defined as the ratio of lengths of its opposite side to its adjacent. i.e, Tanθ = AB/BC • Cotangent Function: The Cotangent ratio for the given angle θ in a right-angled triangle is defined as the ratio of lengths of its adjacent side to its opposite. It’s the reciprocal of the tan ratio. i.e, Cotθ = BC/AB =1/Tanθ • Secant Function: The Secant ratio for the given angle θ in a right-angled triangle is defined as the ratio of lengths of its Hypotenuse side to its adjacent. i.e, Secθ = AC/BC • Cosecant Function: The ...

Trigonometric Identities Email this page to a friend Resources · · · · · · Search Trigonometric Identities ( sin(theta) = a / c csc(theta) = 1 / sin(theta) = c / a cos(theta) = b / c sec(theta) = 1 / cos(theta) = c / b tan(theta) = sin(theta) / cos(theta) = a / b cot(theta) = 1/ tan(theta) = b / a sin(-x) = -sin(x) csc(-x) = -csc(x) cos(-x) = cos(x) sec(-x) = sec(x) tan(-x) = -tan(x) cot(-x) = -cot(x) sin ^2(x) + cos ^2(x) = 1 tan ^2(x) + 1 = sec ^2(x) cot ^2(x) + 1 = csc ^2(x) sin(x y) = sin x cos y cos x sin y cos(x y) = cos x cosy sin x sin y tan(x y) = (tan x tan y) / (1 tan x tan y) sin(2x) = 2 sin x cos x cos(2x) = cos ^2(x) - sin ^2(x) = 2 cos ^2(x) - 1 = 1 - 2 sin ^2(x) tan(2x) = 2 tan(x) / (1 - tan ^2(x)) sin ^2(x) = 1/2 - 1/2 cos(2x) cos ^2(x) = 1/2 + 1/2 cos(2x) sin x - sin y = 2 sin( (x - y)/2 ) cos( (x + y)/2 ) cos x - cos y = -2 sin( (x - y)/2 ) sin( (x + y)/2 ) Trig Table of Common Angles angle 0 30 45 60 90 sin ^2(a) 0/4 1/4 2/4 3/4 4/4 cos ^2(a) 4/4 3/4 2/4 1/4 0/4 tan ^2(a) 0/4 1/3 2/2 3/1 4/0 Given Triangle abc, with angles A,B,C; a is opposite to A, b opposite B, c opposite C: a/sin(A) = b/sin(B) = c/sin(C) (Law of Sines) c ^2 = a ^2 + b ^2 - 2ab cos(C) b ^2 = a ^2 + c ^2 - 2ac cos(B) a ^2 = b ^2 + c ^2 - 2bc cos(A) (Law of Cosines) (a - b)/(a + b) = tan [(A-B)/2] / tan [(A+B)/2] (Law of Tangents) Contact us | Advertising & Sponsorship | Partnership | Link to us © 2000-2005 Math.com. All rights reserved.

The term Trigonometry is derived from Greek words i.e; trigonon and metron, which implies triangle and to measure respectively, θ. There are 6 Trigonometry ratios namely, Sine, Cosine, Tangent, Cotangent, Secant, and Cosecant. These trigonometry ratios tell the different combinations in a right-angled triangle. Trigonometric ratios Trigonometric ratios are ratios of the lengths of the right-angled triangle. These ratios can be used to determine the ratios of any two sides out of a total of three sides of a right-angled triangle. • Sine function: The sine ratio for the given angle θ in a right-angled triangle is defined as the ratio of lengths of its opposite side to its hypotenuse. i.e., Sinθ = AB/AC • Cosine function: The Cosine ratio for the given angle θ in a right-angled triangle is defined as the ratio of lengths of its adjacent side to its hypotenuse. i.e, Cosθ = BC/AC • Tangent Function: The Tangent ratio for the given angle θ in a right-angled triangle is defined as the ratio of lengths of its opposite side to its adjacent. i.e, Tanθ = AB/BC • Cotangent Function: The Cotangent ratio for the given angle θ in a right-angled triangle is defined as the ratio of lengths of its adjacent side to its opposite. It’s the reciprocal of the tan ratio. i.e, Cotθ = BC/AB =1/Tanθ • Secant Function: The Secant ratio for the given angle θ in a right-angled triangle is defined as the ratio of lengths of its Hypotenuse side to its adjacent. i.e, Secθ = AC/BC • Cosecant Function: The ...

Sin Theta Formula Apart from cos and tan, the sine function is an essential trigonometric function. The ratio of the opposite side and the hypotenuse is known as sine theta. Consider the below right-angled triangle ABC, Sin θ = opposite side/hypotenuse = CB/AC If theta is shifted to C from A, then the formula would transform as below Sin θ = opposite side/hypotenuse = AB/AC SIN θ Values The below table shows the values of sin θ for various degrees Sin θ degree value 0 0 30 ½ 45 1√ 2 60 3√ 2 90 1 180 0 Sine Wave The below graph shows how sine wave looks like If we look into calculus the differentiation of sin θ = cos θ whereas on integrating we get – cos θ More Sin Theta Formula • Sin (- D) = – sin D • Sin (90 – R) = cos R • Sin (180 – B) = sin B • sin 2 M + cos 2 M = 1 • A+B =Sin A ×Cos B+Cos A ×Sin B • A-B =Sin A ×Cos B-Cos A ×Sin B • Sin 2 θ = 2 sin θ. cos θ • Sin 3 θ = 3 sin θ – 4 sin 3 θ Solved Examples 1. If cos θ = 24/25 then find the value of sin θ using sin theta formula. We know that, sin² θ + cos² θ = 1 Sin² θ=1- cos² 2. On a building site, John was working. He’s trying to get to the top of the wall. A 44-foot ladder connects the top of the wall to a location on the ground. The ladder forms a 60-degree angle with the ground. What would the wall’s height be? We know that sin 60 = √3/2, also sin θ here in this case would be wall’s height/ladder 3. In a 7,24,25 right angled triangle at B. what would be the value of Sin C ? Sin C = Opposite side/hypotenuse = AB/AC =2...