Trigonometry: Angle Sum and Difference Identities
Read this topicExplanations 6
- A set of helpful identities when working with sines and cosines: sin(α+β)=sin(α)cos(β)+sin(β)cos(α)\sin(\alpha + \beta) = \sin(\alpha)\cos(\beta) + \sin(\beta)\cos(\alpha)s…
By Ray Li, Joshua Siktar, Alexander Wei, Harrison Grodin, Ryan Alweiss, Ahaan Rungta, Daniel Liu, Anusha Rahman
- Here are some useful identities pertaining to sums of angles: sin(x+y)=sin(x)cos(y)+cos(x)sin(y)\sin(x + y) = \sin(x)\cos(y) + \cos(x)\sin(y)sin(x+y)=sin(x)cos(y)+cos(x)sin…
By Joshua Siktar
- Continuing our discussion on these trigonometric function identities, let's now find a formula for sin(A+B)\sin{(A+B)}sin(A+B). The sine area formula for a triangle is: A=12⋅ab…
By Brandon Lin, Gabi Slizewska, Anusha Rahman
- If an angle AAA is a "special angle" like 30∘30^{\circ}30∘ or 45∘45^{\circ}45∘, or AAA is an angle in a right triangle whose side lengths we know, then we can evaluate trig func…
By Holden Lee, Expii Team, Anusha Rahman
- Angle Sum & Difference Identities There are six negative angle identities you need to memorize! Negative angle identities Co-function identities Angle and sum differences identi…
By Anusha Rahman
- (Video) Sum and Difference Identities The Organic Chemistry Tutor In this video by The Organic Chemistry Tutor, you will learn about sum and difference identities in trigonometry.
By Anusha Rahman
Problems 28
- Use the angle addition formulas to calculate each of the following quantities: sin(105∘)\sin(105^{\circ})sin(105∘) cos(105∘)\cos(105^{\circ})cos(105∘) sin(165∘)\sin(165^{\cir…
- What is sin(5π12)\sin(\frac{5\pi}{12})sin(125π)? Hint: sin(A+B)=sin(A)cos(B)+cos(A)sin(B)\sin(A + B) = \sin(A)\cos(B) + \cos(A)\sin(B)sin(A+B)=sin(A)cos(B)+cos(A)sin(B)
- Let x=sin(A)x = \sin(A)x=sin(A). Using the general angle sum identities and the double angle identities, find sin(3A)\sin(3A)sin(3A) in terms of xxx.
- If −1<x<1-1 < x < 1−1<x<1 and −1<y<1-1 < y < 1−1<y<1, define the "relativistic sum'' x⊕yx \oplus yx⊕y to be x⊕y=x+y1+xy.x \oplus y = \frac{x + y}{1 + xy} .x⊕y=1+xyx+y. The oper…
- e712πi=e^{\frac{7}{12} \pi i} =e127πi=
- Find an exact value for sin(75∘)\sin(75^{\circ})sin(75∘).
- Find an exact value for sin(195∘)\sin(195^{\circ})sin(195∘).
- Find an exact value for cos(165∘)\cos(165^{\circ})cos(165∘).
- Find an exact value for cos(345∘)\cos(345^{\circ})cos(345∘).
- Find an exact value for cos(7π12)\cos(\frac{7\pi}{12})cos(127π).
- Find an exact value for cos(π12)\cos(\frac{\pi}{12})cos(12π).
- Find an exact value for sin(5π12)\sin(\frac{5\pi}{12})sin(125π).
- Find an exact value for sin(11π12)\sin(\frac{11\pi}{12})sin(1211π).
- Rewrite in terms of sin(x)\sin(x)sin(x) and cos(x)\cos(x)cos(x). sin(x+11π6)\\\sin(x+\frac{11\pi}6)sin(x+611π)
- Rewrite in terms of sin(x)\sin(x)sin(x) and cos(x)\cos(x)cos(x). cos(x+2π3)\\\cos(x+\frac{2\pi}3)cos(x+32π)
- Rewrite in terms of sin(x)\sin(x)sin(x) and cos(x)\cos(x)cos(x). sin(x−3π4)\\\sin(x-\frac{3\pi}4)sin(x−43π)
- Rewrite in terms of sin(x)\sin(x)sin(x) and cos(x)\cos(x)cos(x). cos(x−5π4)\\\cos(x-\frac{5\pi}4)cos(x−45π)
- Given sin(a)=23\sin(a)=\frac23sin(a)=32 and cos(b)=−14\cos(b)=-\frac14cos(b)=−41, with aaa and bbb both in the interval [π2,π)[\frac{\pi}2,\pi)[2π,π) find sin(a+b)\sin(a+b…
- Given sin(a)=23\sin(a)=\frac23sin(a)=32 and cos(b)=−14\cos(b)=-\frac14cos(b)=−41, with aaa and bbb both in the interval [π2,π)[\frac{\pi}2,\pi)[2π,π) find cos(a−b)\cos(a-b…
- Given sin(a)=45\sin(a)=\frac45sin(a)=54 and cos(b)=13\cos(b)=\frac13cos(b)=31, with aaa and bbb both in the interval [0,π2)[0,\frac{\pi}2)[0,2π) find cos(a+b)\cos(a+b)cos(…
- Given sin(a)=45\sin(a)=\frac45sin(a)=54 and cos(b)=13\cos(b)=\frac13cos(b)=31, with aaa and bbb both in the interval [0,π2)[0,\frac{\pi}2)[0,2π) find sin(a−b)\sin(a-b)sin(…
- Solve for all solutions. sin(3x)cos(6x)−cos(3x)sin(6x)=−0.9\\\sin(3x)\cos(6x)-\cos(3x)\sin(6x)=-0.9sin(3x)cos(6x)−cos(3x)sin(6x)=−0.9
- Solve for all solutions. sin(6x)cos(11x)−cos(6x)sin(11x)=−0.1\\\sin(6x)\cos(11x)-\cos(6x)\sin(11x)=-0.1sin(6x)cos(11x)−cos(6x)sin(11x)=−0.1
- Solve for all solutions. cos(2x)cos(x)+sin(2x)sin(x)=1\\\cos(2x)\cos(x)+\sin(2x)\sin(x)=1cos(2x)cos(x)+sin(2x)sin(x)=1
- Solve for all solutions. cos(5x)cos(3x)−sin(5x)sin(3x)=32\\\cos(5x)\cos(3x)-\sin(5x)\sin(3x)=\frac{\sqrt3}2cos(5x)cos(3x)−sin(5x)sin(3x)=23
- Find the exact value of the following expression: sin105∘\sin105^\circsin105∘
- Find the exact value of the following expression: cos75∘\cos75^\circcos75∘
- Find the exact value of the following expression: sin120∘\sin120^\circsin120∘