Which equation represents the values in the table?

adell [148]

Your answer is B or #2 out of the possible answers

6 0

2 years ago

Considering only the values of β for which sinβtanβsecβcotβ is defined, which of the following expressions is equivalent to sinβ

-Dominant- [34]

Answer:

$\tan(\beta)$

Step-by-step explanation:

For many of these identities, it is helpful to convert everything to sine and cosine, see what cancels, and then work to build out to something. If you have options that you're building toward, aim toward one of them.

${\tan(\theta)}={\dfrac{\sin(\theta)}{\cos(\theta)}$ and ${\sec(\theta)}={\dfrac{1}{\cos(\theta)}$

Recall the following reciprocal identity:

$\cot(\theta)=\dfrac{1}{\tan(\theta)}=\dfrac{1}{ \left ( \dfrac{\sin(\theta)}{\cos(\theta)} \right )} =\dfrac{\cos(\theta)}{\sin(\theta)}$

So, the original expression can be written in terms of only sines and cosines:

$\sin(\beta)\tan(\beta)\sec(\beta)\cot(\beta)$

$\sin(\beta) * \dfrac{\sin(\beta) }{\cos(\beta) } * \dfrac{1 }{\cos(\beta) } * \dfrac{\cos(\beta) } {\sin(\beta) }$

$\sin(\beta) * \dfrac{\sin(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}}{\cos(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}} * \dfrac{1 }{\cos(\beta) } * \dfrac{\cos(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}} {\sin(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}}$

$\sin(\beta) *\dfrac{1 }{\cos(\beta) }$

$\dfrac{\sin(\beta)}{\cos(\beta) }$

Working toward one of the answers provided, this is the tangent function.

The one caveat is that the original expression also was undefined for values of beta that caused the sine function to be zero, whereas this simplified function is only undefined for values of beta where the cosine is equal to zero. However, the questions states that we are only considering values for which the original expression is defined, so, excluding those values of beta, the original expression is equivalent to $\tan(\beta)$ .

8 0

2 years ago

X + y = 24

Masja [62]

Answer:

(10, 14)

Step-by-step explanation:

To solve this system let's use substitution:

Solve the first equation for x, obtaining x = 24 - y, and then substitute 24 - y for x in the second equation:

3(24 - y) + 5y = 100

Performing the indicated multiplication, we get:

72 - 3y + 5y = 100

Combining like terms results in 72 - 100 = -2y, or -28 = -2y

Thus, y must be 14.

If y = 14, then the first equation tells us that x = 10.

Check: Is this true? 3(10) + 5(14) = 100 YES

The solution is (10, 14).

What was it about the questions on the best that you were supposed to compare to this solution?

8 0

3 years ago

Joe bought 16 pounds of flour for $7.<br> How many pounds of flour did he get per dollar?

wolverine [178]

Answer:

112

Step-by-step explanation:

7 0

3 years ago

In circle P with mNRQ = 60°, find the angle measure of minor arc NQ

Galina-37 [17]

Given:

m∠NRQ = 60°

To find:

The angle measure of minor arc NQ

Solution:

The inscribed angle is half of the intercepted arc.

$$\Rightarrow m\angle NRQ =\frac{1}{2} m(ar NQ)$

Multiply by 2 on both sides.

$$\Rightarrow 2 \times m\angle NRQ =2 \times \frac{1}{2} m(ar NQ)$

$$\Rightarrow 2 \ m\angle NRQ =m(ar NQ)$

Substitute m∠NRQ = 60°.

$$\Rightarrow 2\times 60^\circ=m(ar NQ)$

$$\Rightarrow 120^\circ=m(ar NQ)$

The measure of minor arc NQ is 120°.

8 0

3 years ago