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3 years ago

If sin theta = 1/2 and pi/2 < theta < pi , what are the values of cos and tan?

Mathematics

1 answer:

zhannawk [14.2K]3 years ago

5 0

Answer:

cos(θ) = -(√3)/2
tan(θ) = -(√3)/3

Step-by-step explanation:

Referring to the attached short table of trig functions, we see that the reference angle with sin(θ) = 1/2 is π/6. The table also shows cosine and tangent values for that angle.

In the second quadrant, where π/2 < θ < π, the cosine and tangent are both negative. The values you seek are ...

cos(θ) = -(√3)/2

tan(θ) = -1/√3 = -(√3)/3

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If sin θ = cot θ, then, what is the value of cos θ + 2 cos^2 θ + 2 cos^3 θ + cos^ 4 θ ?

VARVARA [1.3K]

Notice that

cos(θ) + 2 cos²(θ) + 2 cos³(θ) + cos⁴(θ)

= cos(θ) (1 + 2 cos(θ) + 2 cos²(θ) + cos³(θ))

= cos(θ) ([1 + cos(θ)] + [cos(θ) + cos²(θ)] + [cos²(θ) + cos³(θ)])

= cos(θ) ([1 + cos(θ)] + [cos(θ) (1 + cos(θ))] + [cos²(θ) (1 + cos(θ))])

= cos(θ) (1 + cos(θ)) (1 + cos(θ) + cos²(θ))

Given that sin(θ) = cot(θ), by definition of cotangent this tells us that

sin(θ) = cos(θ)/sin(θ) ⇒ cos(θ) = sin²(θ)

and by the Pythagorean identity

cos²(θ) + sin²(θ) = 1

it follows that

cos(θ) = sin²(θ) = 1 - cos²(θ)

Substituting these results into the factorization above gives

cos(θ) (1 + cos(θ)) (1 + cos(θ) + cos²(θ))

= cos(θ) (1 + cos(θ)) (1 + [1 - cos²(θ)] + cos²(θ))

= 2 cos(θ) (1 + cos(θ))

= 2 sin²(θ) (1 + cos(θ))

= 2 (1 - cos²(θ)) (1 + cos(θ))

= 2 (1 + cos(θ) - cos²(θ) - cos³(θ))

= 2 (cos(θ) + cos(θ) - cos³(θ))

= 2 (2 cos(θ) - cos³(θ))

= 2 cos(θ) (2 - cos²(θ))

= 2 cos(θ) (1 + cos(θ))

= 2 (cos(θ) + cos²(θ))

= 2 (1 - cos²(θ) + cos²(θ))

= 2

7 0

3 years ago

PLEASE HELP FAST

Igoryamba

5 + (-10) = 5 - 10
= -5 .

5 + (-3) = 5 -3
=2 .

5 + 3 = 8 .

5 + 0 = 5 .

8 0

4 years ago

Finish the sentence.<br> Pack in the mail, _________

Ostrovityanka [42]

Answer:it gone hum????

Step-by-step explanation:is that dababy

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3 years ago

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Three friends went out to eat dinner the bill came to 35.60 the three friends also decided to leave a 6.00 tip if they shared th

vfiekz [6]

Answer:

13.87

Step-by-step explanation:

Three friends went out to eat dinner the bill came to 35.60. This means that the total bill for the dinner was 35.60.

The original bill was 35.60. If they shared the bill equally, the amount that each of them would pay would be

Total bill / number of friends

It becomes 35.60/3 = 11.87

The three friends also decided to leave a 6.00 tip and it was sent equally. This means that each friend would pay a tip of

6/3 = 2. ( total amount of tip paid divided by the number of friends)

Therefore, the total amount that each has to pay = amount each paid for the bill + amount that each paid for the tip

= 11.87 + 2 = 13.87

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3 years ago

Evaluate In 7 (alg 2)

eduard

Answer:

i'm not sure what you need help with.

Step-by-step explanation:

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3 years ago

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