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Cosine:
cos(A+B) = cosAcosB-sinAsinB

Sine:
sin(A+B) = sinAcosB + cosAsinB

Tangent:
tan(A+B) = (tanA + tanB)/(1-tanAtanB)

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Sine:
sin(A-B) = sinAcosB - cosAsinB

Cosine:
cos(A-B) = cosAcosB + sinAsinB

Tangent:
tan(A-B) = (tanA - tanB)/(1 + tanAtanB)

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sine:
sin2 θ = 2sin θcos θ

cosine:
cos2 θ= cos^2 θ - sin^2 θ
or
cos^2 θ = 1 - 2sin^2 θ
or
cos^2 θ = 2cos^2 θ - 1

Tangent:
tan2 θ = 2 tan θ/1-tan^2 θ

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c^2= a^2 + b^2 - 2abcosC

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sinA/a = sinB/b = sinC/c

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I used to think that when solving a triangle, each angle only had one possible answer. Now I know that an angle can have multiple answers. 

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I used to think that when solving a triangle, each angle only had one possible answer. Now I know that an angle can have multiple answers. 

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I used to think that sin(2A) could just be the same as 2sinA, but now I know that that's not the case.

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I used to think that sin(2A) could just be the same as 2sinA, but now I know that that's not the case.

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I used to think that sin(A-B)=sinA-sinB, but now I know that is not the case

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I used to think that sin(A-B)=sinA-sinB, but now I know that is not the case

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Area of a Triangle/Area of a Parallelogram

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Area of a Triangle/Area of a Parallelogram

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Triangle:
k= 1/2 * bc * sinA
k= 1/2 * ab * sinC
k= 1/2 * ac * sinB

Parallelogram:
k= 2(1/2*ab*sinC)
k= 2(1/2*bc*sinA)
k= 2(1/2*ac*sinB)

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Key Concept: Finding The side lengths and angle measurements of a triangle using Law of Sines and Law of Cosines.

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Key Concept: Finding The side lengths and angle measurements of a triangle using Law of Sines and Law of Cosines.

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Through the application of the law of sines, you can find find the angle meausrements and side lengths of a triangle.

If you are not given a corresponding angle and side measurement, then you can use the law of cosines to find either the angle measurement or side length.

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Identities used to find the cosine, sine, or tangent of the sum of two angles. They help us to break down and solve angles that wouldn't be used in 30-60-90 triangles or right triangles.

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Identities used to find the cosine, sine, or tangent of the difference of two angles. THey help us to break down and solve angles that don't belong to 30-60-90 or right triangles.

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The law of sines defines the relationship between the side lengths and angles on a triangle. The ratio of a sines length and angle must be the same for all 3 corresponding sides/angles.

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The law of cosines identifies the third side length on a triangle when the other two sides and the sides angle measurement is known.

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Double angle formulas allow us to write a given angle measurement as 2 θ and then rewrite this identity as a different value more friendly to the expression. This makes it easier to break down and solve the expression.

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I used to think that you can choose when to use law of cosine and law of sin but now I know that you generally use law of sin to find a missing angle and law of cosine to find missing side length.

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I used to think that you can choose when to use law of cosine and law of sin but now I know that you generally use law of sin to find a missing angle and law of cosine to find missing side length.

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Problem #2: Law of Sines and area of a Triangle

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Problem #2: Law of Sines and area of a Triangle

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In triangle XYZ, angle Z = 105 degrees, angle Y = 38 degrees, and y=5 units. Find the missing side lengths, angle measurements, and calculate the area.

Answers:
z = 7.84 units
x = 4.89 units
angle X = 37 degrees
Area = 11.81 units squared

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Problem #3: Law of Cosines and Law of Sines

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Problem #3: Law of Cosines and Law of Sines

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Find all angle measurements of triangle ABC if a=11, b=12, and c=13.

Answers:
angle C = 68.72 degrees
angle A = 52 degrees
angle B = 59.28 degrees

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Problem #4 Sum and Difference Identities

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Problem #4 Sum and Difference Identities

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cos(2x)-cosx-1=0

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Half-angle formulas allow us to write a given a given angle measurement as 1/2 θ and then lets us rewrite this identity as a different value that's more friendly to the expression, making the expression easier to break down and solve.

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A connection I made was to Unit 2 with the Pythagorean Identities.

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A connection I made was to Unit 2 with the Pythagorean Identities.

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A connection I made to unit 2 is sin is positive in quadrants 1 and 2 and negative in quadrants 3 and 4. 

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A connection I made to unit 2 is sin is positive in quadrants 1 and 2 and negative in quadrants 3 and 4. 

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A connection I made to unit 2 is doing sine cosine and tangent equations with multiple layers. Those are the more interesting problems, but they're also hard.

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A connection I made to unit 2 is doing sine cosine and tangent equations with multiple layers. Those are the more interesting problems, but they're also hard.

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Just like in Unit 2, we would occasionaly use proofs to show that an expression is equivilent to an identity/function.

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Just like in Unit 2, we would occasionaly use proofs to show that an expression is equivilent to an identity/function.

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These formulas allow us to find the areas of triangles. They are especially useful for helping us find the area of a triangle that does not have a 90 degree angle.

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Key Idea: Naming angles and sides of triangles.

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Key Idea: Naming angles and sides of triangles.

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Every vertice of a triangle (angle) is named using a capital letter (Ex: A).
The corresponding side to this angle is labeled using the lowercase version of that letter (ex. a).

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Vertices are a triangles angles. They are labeled using capital letters and a triangles name is defined by these letters.

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Problem #6: Proof using a double angle formula

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Problem #6: Proof using a double angle formula