1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Alinara [238K]
3 years ago
11

In Exercises 5-7, find all the exact t-values for which the given statement is true,

Mathematics
1 answer:
bearhunter [10]3 years ago
4 0

Answer:  See Below

<u>Step-by-step explanation:</u>

NOTE: You need the Unit Circle to answer these (attached)

5) cos (t) = 1

Where on the Unit Circle does cos = 1?

Answer: at 0π (0°) and all rotations of 2π (360°)

In radians:     t = 0π + 2πn

In degrees:   t = 0° + 360n

******************************************************************************

6)\quad sin (t) = \dfrac{1}{2}

Where on the Unit Circle does   sin = \dfrac{1}{2}

<em>Hint: sin is only positive in Quadrants I and II</em>

\text{Answer: at}\  \dfrac{\pi}{6}\ (30^o)\ \text{and at}\ \dfrac{5\pi}{6}\ (150^o)\ \text{and all rotations of}\ 2\pi \ (360^o)

\text{In radians:}\ t = \dfrac{\pi}{6} + 2\pi n \quad \text{and}\quad \dfrac{5\pi}{6} + 2\pi n

In degrees:    t = 30° + 360n  and  150° + 360n

******************************************************************************

7)\quad tan (t) = -\sqrt3

Where on the Unit Circle does    \dfrac{sin}{cos} = \dfrac{-\sqrt3}{1}\ or\ \dfrac{\sqrt3}{-1}\quad \rightarrow \quad (1,-\sqrt3)\ or\ (-1, \sqrt3)

<em>Hint: sin and cos are only opposite signs in Quadrants II and IV</em>

\text{Answer: at}\  \dfrac{2\pi}{3}\ (120^o)\ \text{and at}\ \dfrac{5\pi}{3}\ (300^o)\ \text{and all rotations of}\ 2\pi \ (360^o)

\text{In radians:}\ t = \dfrac{2\pi}{3} + 2\pi n \quad \text{and}\quad \dfrac{5\pi}{3} + 2\pi n

In degrees:    t = 120° + 360n  and  300° + 360n

You might be interested in
Boxes of cereal normally cost £2.89 each, but a supermarket has a special offer: Boxes of Cereal 3 for the price of 2
Agata [3.3K]

Answer:

9 boxes

Step-by-step explanation:

Boxes of Cereal 3 for the price of 2, the the price of the 3 boxes of cereals must be : 2 × £2.89 = £5.78

Boxes Megan can buy for the offer = £20 ÷ £5.78  = 3.46 (to 3 s.f.)≈ 3

3 × 3 =9 packs

But they actually only cost : 3 × £5.78  = £17.34

Therefore after buying the offer Megan has £20 - £17.34 = £ 2.66 left, which is not enough to buy a single pack, so the answer is 9.

5 0
3 years ago
Please answer ALL of the following if you do so i will give you brainiest :))))) :
chubhunter [2.5K]
2x^2 if x=1/8 is 1/16
4x^2 if x=1/8 is 1/2
8 0
2 years ago
Read 2 more answers
How many times larger is 9 x 10^9 than 3 x 10^-4?
andrezito [222]
The larger value is 9 x 10^9
The smaller value is 3 x 10^(-4)

Divide the larger over the smaller
Doing so will have you divide the coefficients 9 and 3 (numbers in front of the "times ten to the..." portions) to get 9/3 = 3. 
Then you'll also subtract the exponents: 9 minus (-4) = 9 - (-4) = 9 + 4 = 13

In summary so far, we got a coefficient of 3 and an exponent of 13

So the final answer is 3 x 10^13 (assuming you want scientific notation)

If you want to convert to standard notation, instead of scientific notation, move the decimal point in 3.0 thirteen spots to the right to get 

30,000,000,000,000

there are 13 zeros (four groups of 3 plus one just after the 3) in that value above. This is the number 30 trillion
8 0
3 years ago
Natasha has four nickels to dimes and 6 quarters in her pocket what is a theological probability that she will randomly select a
My name is Ann [436]

Answer:

1/2

Step-by-step explanation:

There are 4 nickels, 2 dimes, and 6 quarters. That means a total of 12 coins, half of which are quarters.

(realistically, if she wanted to, she could probably get a quarter every time if she felt for the size)

4 0
3 years ago
Read 2 more answers
What is the base of a triangle that has a height of 6 centimeters and an area of 18 centimeters? Use the formula , where A repre
harina [27]

Answer:

The base of the triangle is 6cm.

Step-by-step explanation:

The find the base of a triangle, use this formula.

Formula : 1/2 x b x h

<em>If you would like some more explanation, see the attached image.</em>

5 0
3 years ago
Other questions:
  • What is the answer and steps to 3 divided by 2/5
    9·2 answers
  • 2a+4(7+5a)<br>I need simplify that, can u guys help me??
    11·2 answers
  • Approximately what percentage of energy transfers to the next food chain level?
    7·1 answer
  • Given triangle JKL find m
    11·1 answer
  • diana charges $10 for a house call plus $35 an hour for electric work.If she made $150 on one job,how many hours did she work​
    12·2 answers
  • Which is bigger, 9/17 or 5/6?
    9·1 answer
  • What is <br> 2(d + 9) <br> I need help on it please and thanks :)
    8·1 answer
  • The diagonals of a quadrilateral QRST intersect at P(2,3). QRST has vertices at Q(3,6) and R(-3,5). What must be the coordinates
    14·1 answer
  • Mr. quick bought new computer system. The regular price was 1,580 , but he got a 15% discount. How much did he actually pay?
    15·1 answer
  • Find the value of the trigonometric ratio.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!