s2w4 Precalc FC Laws of sine and cosine

1

one of the reasons to use identities is so you can rewrite an equation so that there is only one trig function involved. rewrite this equation so that is is only one trig function

1

Is the following an identity?

yes

no

1

Lets review congruent vs similar triangles - what is the difference?

1

Lets review congruent triangles: you know two triangles are congruent if

you have any two sides and an angle, or any two angle and a side, or all three sides

You have at least two sides and one angle or a side and know it is a right triangle

Any two angles and a side, all three sides, or two sides and the angle between those two sides

you have to know all three sides and one angle

1

The angles of a triangle add up to

90

180

270

360

1

ok, up until know, trig has been all about the right triangles. But we are about to push a little beyond that. This is called the law of sines

for ANY triangle, where A is the side opposite angle a, B is the side opposite angle b, and C is the side opposite angle C. Given this triangle with sides a, b and c, drag A B and C to their proper angles.

Mmuae Afoforo a Wobɛpaw:

C

B

A

1

Lets go over why SSA is the "ambiguous case" You will see at the top of this image a line. there is a line segment connected to this line at 31.9°, and the line segment is length 0. So far we do not have a triangle, but we do have

two sides and one angle

one angle, one side, and one line where an unknown part of that line is our side

two sides and two angles

two lines, and angle between them and a dot that must be where the last side of the triangle will go.

1

There is also a law of cosines. it is SIGNIFICANTLY uglier
where c is the angle opposite B.
you might want to pause now and go practice law of sines in aleks homework and the modules.

1

Given the following information about a triangle, which law can you use to find all the other sides?

Side, angle, side
Angle, side, angle
angle, angle, side
side, side, angle
side, side, side
angle, angle, angle

Law of sines
Law of cosines
this does not describe just one triangle

Questions 23 & 22

02:15

Question 24

01:34

3

1

draw the triangle described above. to find the area of the triangle, you need to find the height, how can you do that?

1

watching the proofs helps me understand the laws

true

false

1

categorize

what the law of sines is
what the law of cosines is
when to use the law of sines
when to use the law of cosines
how to simplify or rearrange trig expressions using the identities I know
when are triangles congruent
why SSA gives an ambiguous case
how to use the law of sin to find the area of triangle

ive got this
im fuzzy
so confused

s2w4 Precalc FC Laws of sine and cosine

one of the reasons to use identities is so you can rewrite an equation so that there is only one trig function involved. rewrite this equation so that is is only one trig function

Is the following an identity?

Lets review congruent vs similar triangles - what is the difference?

Lets review congruent triangles: you know two triangles are congruent if

The angles of a triangle add up to

Lets go over why SSA is the "ambiguous case" You will see at the top of this image a line. there is a line segment connected to this line at 31.9°, and the line segment is length 0. So far we do not have a triangle, but we do have

There is also a law of cosines. it is SIGNIFICANTLY uglierwhere c is the angle opposite B. you might want to pause now and go practice law of sines in aleks homework and the modules.

Given the following information about a triangle, which law can you use to find all the other sides?

draw the triangle described above. to find the area of the triangle, you need to find the height, how can you do that?

watching the proofs helps me understand the laws

categorize

one of the reasons to use identities is so you can rewrite an equation so that there is only one trig function involved. rewrite this equation so that is is only one trig function

Is the following an identity?

Lets review congruent vs similar triangles - what is the difference?

Lets review congruent triangles: you know two triangles are congruent if

The angles of a triangle add up to

These two triangles are congruent by

These two triangles are congruent by

These two triangles are congruent by

These two triangles are congruent by

These two triangles are congruent by

These two triangles are congruent by

Lets go over why SSA is the "ambiguous case" You will see at the top of this image a line. there is a line segment connected to this line at 31.9°, and the line segment is length 0. So far we do not have a triangle, but we do have

I know the second side i want is 4, so to construct my 31.9°, 6,4 triangle, I draw a circle of radius four around my point B. How many times does that circle touch my line?

Name the two triangles in my diagram that have a 31.9° angle, and two sides, 4 and 6 units long

setting up Law of Sine's here, I getANDWhat do you think the relationship is between angle BCD and angle BDA is?

At what angle would the radius of circle B only touch that initial line once?

There is also a law of cosines. it is SIGNIFICANTLY uglierwhere c is the angle opposite B. you might want to pause now and go practice law of sines in aleks homework and the modules.

Given the following information about a triangle, which law can you use to find all the other sides?

draw the triangle described above. to find the area of the triangle, you need to find the height, how can you do that?

watching the proofs helps me understand the laws

categorize

These two triangles are congruent by

These two triangles are congruent by

These two triangles are congruent by

These two triangles are congruent by

These two triangles are congruent by

These two triangles are congruent by

I know the second side i want is 4, so to construct my 31.9°, 6,4 triangle, I draw a circle of radius four around my point B. How many times does that circle touch my line?

Name the two triangles in my diagram that have a 31.9° angle, and two sides, 4 and 6 units long

setting up Law of Sine's here, I getANDWhat do you think the relationship is between angle BCD and angle BDA is?

At what angle would the radius of circle B only touch that initial line once?

There is also a law of cosines. it is SIGNIFICANTLY uglier
where c is the angle opposite B.
you might want to pause now and go practice law of sines in aleks homework and the modules.

setting up Law of Sine's here, I get
AND
What do you think the relationship is between angle BCD and angle BDA is?

There is also a law of cosines. it is SIGNIFICANTLY uglier
where c is the angle opposite B.
you might want to pause now and go practice law of sines in aleks homework and the modules.

setting up Law of Sine's here, I get
AND
What do you think the relationship is between angle BCD and angle BDA is?