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Lady bird [3.3K]

2 years ago

9

A.-2b.2c.1d.-1 e.-6plz help being timed will mark brainliest

1 answer:

rusak2 [61]2 years ago

6 0

Answer:

-2 and -1

Step-by-step explanation:

The range would be inside the red half circle and since it is below the horizontal middle line, it is negative. Both -1 and -2 are in the range of the red half circle, both of them are the answer

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For 0 ≤ ϴ < 2π, how many solutions are there to tan(StartFraction theta Over 2 EndFraction) = sin(ϴ)? Note: Do not include va

Black_prince [1.1K]

Answer:

3 solutions:

$\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}$

Step-by-step explanation:

So, first of all, we need to figure the angles that cannot be included in our answers out. The only function in the equation that isn't defined for some angles is $tan(\frac{\theta}{2})$ so let's focus on that part of the equation first.

We know that:

$tan(\frac{\theta}{2})=\frac{sin(\frac{\theta}{2})}{cos(\frac{\theta}{2})}$

therefore:

$cos(\frac{\theta}{2})\neq0$

so we need to find the angles that will make the cos function equal to zero. So we get:

$cos(\frac{\theta}{2})=0$

$\frac{\theta}{2}=cos^{-1}(0)$

$\frac{\theta}{2}=\frac{\pi}{2}+\pi n$

or

$\theta=\pi+2\pi n$

we can now start plugging values in for n:

$\theta=\pi+2\pi (0)=\pi$

if we plugged any value greater than 0, we would end up with an angle that is greater than $2\pi$ so, that's the only angle we cannot include in our answer set, so:

$\theta\neq \pi$

having said this, we can now start solving the equation:

$tan(\frac{\theta}{2})=sin(\theta)$

we can start solving this equation by using the half angle formula, such a formula tells us the following:

$tan(\frac{\theta}{2})=\frac{1-cos(\theta)}{sin(\theta)}$

so we can substitute it into our equation:

$\frac{1-cos(\theta)}{sin(\theta)}=sin(\theta)$

we can now multiply both sides of the equation by $sin(\theta)$

so we get:

$1-cos(\theta)=sin^{2}(\theta)$

we can use the pythagorean identity to rewrite $sin^{2}(\theta)$ in terms of cos:

$sin^{2}(\theta)=1-cos^{2}(\theta)$

so we get:

$1-cos(\theta)=1-cos^{2}(\theta)$

we can subtract a 1 from both sides of the equation so we end up with:

$-cos(\theta)=-cos^{2}(\theta)$

and we can now add $cos^{2}(\theta)$

to both sides of the equation so we get:

$cos^{2}(\theta)-cos(\theta)=0$

and we can solve this equation by factoring. We can factor $cos(\theta)$ to get:

$cos(\theta)(cos(\theta)-1)=0$

and we can use the zero product property to solve this, so we get two equations:

Equation 1:

$cos(\theta)=0$

$\theta=cos^{-1}(0)$

$\theta={\frac{\pi}{2}, \frac{3\pi}{2}}$

Equation 2:

$cos(\theta)-1=0$

we add a 1 to both sides of the equation so we get:

$cos(\theta)=1$

$\theta=cos^{-1}(1)$

$\theta=0$

so we end up with three answers to this equation:

$\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}$

7 0

2 years ago

5. A hockey player whose initial speed is 8.1 m/s increases his speed to 8.6 m/s in order to get to

balu736 [363]

Answer:

0.1m/s²

Step-by-step explanation:

the explanation is in the picture

please rate and mark as brainliest

5 0

2 years ago

Help me please ???!!!!!!!!!!!

pychu [463]

The answer is b

Glllllll

4 0

2 years ago

The lemonade cooler at the class picnic holds 12.5L. One liter is approximately equal to 0.26 gallons. How many gallons does the

lora16 [44]

Answer: There are 3.25 or 3 1/4 gallons in one cooler

Step-by-step explanation:

If one liter is appx .26 gallons we need to multiply the number of liters there are. So 12.5 times .26 to get the answer 3.25

4 0

3 years ago

Mickey deposits $500 into an account that earns 7% interest. How much is in the account after one year?

Klio2033 [76]

If it's annual:

7% of 500 is 35 so add 35 to 500 and you get 535.

4 0

3 years ago