Unit 3 and 4 Padlet by John Tully https://padlet.com/jmtully1/qm2vz6ofkx7ip16k Jack, Elliot, Jonah, and Evan en-us 2020-12-02 18:16:33 UTC 2026-01-21 05:07:08 UTC hello@padlet.com Half Angle Formulas ewkatsanis1 https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/981037182 2020-12-02 18:20:50 UTC https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/981037182 Sum Formulas eopersell1 https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/981038020 Cosine: 
cos(A+B) = cosAcosB-sinAsinB

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

Tangent:
tan(A+B) = (tanA + tanB)/(1-tanAtanB)]]> 2020-12-02 18:21:00 UTC https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/981038020 Double Angle Identities jmtully1 https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/981050333 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


]]> 2020-12-02 18:23:27 UTC https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/981050333 Law of cosines jfross4 https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/981062851 c^2= a^2 + b^2 - 2abcosC]]> 2020-12-02 18:26:01 UTC https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/981062851 Law of sines jfross4 https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/981069867 sinA/a = sinB/b = sinC/c]]> 2020-12-02 18:27:18 UTC https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/981069867 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. jmtully1 https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/981096200 2020-12-02 18:32:35 UTC https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/981096200 I used to think that sin(2A) could just be the same as 2sinA, but now I know that that's not the case. eopersell1 https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/981102912 2020-12-02 18:33:54 UTC https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/981102912 Area of a Triangle/Area of a Parallelogram jmtully1 https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/992670109 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)]]> 2020-12-07 03:06:42 UTC https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/992670109 Key Concept: Finding The side lengths and angle measurements of a triangle using Law of Sines and Law of Cosines. jmtully1 https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/996623857 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.]]> 2020-12-08 01:44:11 UTC https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/996623857 Difference Identities jmtully1 https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/996631504 Sine:
sin(A-B) = sinAcosB - cosAsinB

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

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

]]> 2020-12-08 01:48:00 UTC https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/996631504 Sum Identities jmtully1 https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1000748915 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.]]> 2020-12-09 02:32:20 UTC https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1000748915 Difference Identities jmtully1 https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1000759768 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.]]> 2020-12-09 02:38:02 UTC https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1000759768 Law of Sines jmtully1 https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1000764133 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.]]> 2020-12-09 02:40:30 UTC https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1000764133 Law of Cosines jmtully1 https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1000764271 The law of cosines identifies the third side length on a triangle when the other two sides and the sides angle measurement is known.]]> 2020-12-09 02:40:35 UTC https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1000764271 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. jfross4 https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1003299012 2020-12-09 17:52:51 UTC https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1003299012 I used to think that sin(A-B)=sinA-sinB, but now I know that is not the case ewkatsanis1 https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1003323623 2020-12-09 17:57:57 UTC https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1003323623 Problem #1: Half Angle Formulas eopersell1 https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1003343080 2020-12-09 18:01:53 UTC https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1003343080 Problem #2: Law of Sines and area of a Triangle jmtully1 https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1003352987 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]]> 2020-12-09 18:03:57 UTC https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1003352987 Problem #3: Law of Cosines and Law of Sines jmtully1 https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1003355166 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]]> 2020-12-09 18:04:24 UTC https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1003355166 Problem #4 Sum and Difference Identities jfross4 https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1003360933 2020-12-09 18:05:35 UTC https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1003360933 Problem #5: Double Angle Formulas ewkatsanis1 https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1003367534 cos(2x)-cosx-1=0]]> 2020-12-09 18:06:50 UTC https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1003367534 Double Angle Formulas jmtully1 https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1008903284 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.]]> 2020-12-11 05:03:44 UTC https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1008903284 A connection I made was to Unit 2 with the Pythagorean Identities. ewkatsanis1 https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1010711683 2020-12-11 17:51:17 UTC https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1010711683 A connection I made to unit 2 is sin is positive in quadrants 1 and 2 and negative in quadrants 3 and 4. jfross4 https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1010713080 2020-12-11 17:51:35 UTC https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1010713080 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. eopersell1 https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1010756459 2020-12-11 18:01:35 UTC https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1010756459 Half Angle Formulas ewkatsanis1 https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1010789639 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.]]> 2020-12-11 18:09:01 UTC https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1010789639 Just like in Unit 2, we would occasionaly use proofs to show that an expression is equivilent to an identity/function. jmtully1 https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1011680554 2020-12-11 23:48:20 UTC https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1011680554 Area of a Triangle Formula jmtully1 https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1011688154 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.]]> 2020-12-11 23:55:15 UTC https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1011688154 Key Idea: Naming angles and sides of triangles. jmtully1 https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1011747827 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).]]> 2020-12-12 00:58:47 UTC https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1011747827 Vertices jmtully1 https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1011754055 Vertices are a triangles angles. They are labeled using capital letters and a triangles name is defined by these letters.]]> 2020-12-12 01:05:50 UTC https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1011754055 Problem #6: Proof using a double angle formula jmtully1 https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1011771596 2020-12-12 01:27:09 UTC https://padlet.com/jmtully1/qm2vz6ofkx7ip16k/wish/1011771596