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Talja [164]
3 years ago
11

CAN SOMEONE PLEASE HELP ME WITH THIS ITS DUE TODAY :)))

Mathematics
2 answers:
Tresset [83]3 years ago
8 0
I would but I don’t know how to explain it all!
Crank3 years ago
7 0
I have really bad eye sight but I know mad really well can you write out the ones you need
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This is finding exact values of sin theta/2 and tan theta/2. I’m really confused and now don’t have a clue on how to do this, pl
Lostsunrise [7]

First,

tan(<em>θ</em>) = sin(<em>θ</em>) / cos(<em>θ</em>)

and given that 90° < <em>θ </em>< 180°, meaning <em>θ</em> lies in the second quadrant, we know that cos(<em>θ</em>) < 0. (We also then know the sign of sin(<em>θ</em>), but that won't be important.)

Dividing each part of the inequality by 2 tells us that 45° < <em>θ</em>/2 < 90°, so the half-angle falls in the first quadrant, which means both cos(<em>θ</em>/2) > 0 and sin(<em>θ</em>/2) > 0.

Now recall the half-angle identities,

cos²(<em>θ</em>/2) = (1 + cos(<em>θ</em>)) / 2

sin²(<em>θ</em>/2) = (1 - cos(<em>θ</em>)) / 2

and taking the positive square roots, we have

cos(<em>θ</em>/2) = √[(1 + cos(<em>θ</em>)) / 2]

sin(<em>θ</em>/2) = √[(1 - cos(<em>θ</em>)) / 2]

Then

tan(<em>θ</em>/2) = sin(<em>θ</em>/2) / cos(<em>θ</em>/2) = √[(1 - cos(<em>θ</em>)) / (1 + cos(<em>θ</em>))]

Notice how we don't need sin(<em>θ</em>) ?

Now, recall the Pythagorean identity:

cos²(<em>θ</em>) + sin²(<em>θ</em>) = 1

Dividing both sides by cos²(<em>θ</em>) gives

1 + tan²(<em>θ</em>) = 1/cos²(<em>θ</em>)

We know cos(<em>θ</em>) is negative, so solve for cos²(<em>θ</em>) and take the negative square root.

cos²(<em>θ</em>) = 1/(1 + tan²(<em>θ</em>))

cos(<em>θ</em>) = - 1/√[1 + tan²(<em>θ</em>)]

Plug in tan(<em>θ</em>) = - 12/5 and solve for cos(<em>θ</em>) :

cos(<em>θ</em>) = - 1/√[1 + (-12/5)²] = - 5/13

Finally, solve for sin(<em>θ</em>/2) and tan(<em>θ</em>/2) :

sin(<em>θ</em>/2) = √[(1 - (- 5/13)) / 2] = 3/√(13)

tan(<em>θ</em>/2) = √[(1 - (- 5/13)) / (1 + (- 5/13))] = 3/2

3 0
2 years ago
Jeremy spent $26.50 for 5.5lb. What would be the price of 1 pound of dog food
NikAS [45]

Answer:

$4.81

Step-by-step explanation:

4 0
3 years ago
Which are partial products for 89 × 25?
Keith_Richards [23]
D is the answer. hth.
6 0
3 years ago
Read 2 more answers
Fill in the boxes please
IRINA_888 [86]

Answer:

x=12, DO=45O, G=45, DG=90

Step-by-step explanation:

Mid point means both lenghts are equal

4x-3=2x+21

2x=24

X=12

-----------------

1)4(12)-3=48-3=45

2)2(12)+21=24+21=45

-----------------------------

DO=45

OG=45

DG=90

4 0
3 years ago
Read 2 more answers
In this excerpt the servant is a comic figure because he unknowingly invites his master
dedylja [7]

Answer:

Yes he would be

3 0
3 years ago
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