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
Reil [10]
3 years ago
5

If sine ⁡theta equals negative 8/17 and the terminal side of theta lies in quadrant IV, find cosine ⁡ theta .

Mathematics
1 answer:
Lelechka [254]3 years ago
3 0
\sin^2\theta+\cos^2\theta=1\implies \cos\theta=\pm\sqrt{1-\sin^2\theta}

Since \sin\theta=-\dfrac8{17}, it follows that

\cos\theta=\pm\sqrt{1-\dfrac{64}{289}}=\pm\sqrt{\dfrac{225}{289}}=\pm\dfrac{15}{17}

where the sign depends on the location of the terminal side of the angle. Since the terminal side lies in the fourth quadrant, that means the cosine of the angle is positive, so

\cos\theta=\dfrac{15}{17}
You might be interested in
A game starts by flipping a coin. If you get heads, then you get to roll a die and, if you roll a 4, you win the jackpot. If you
Mariana [72]

\frac{5}{24}

Step-by-step explanation:

There are two ways to win a jackpot.

Let p_{1} be the probability for first method and p_{2} be the probability for second method.

Probability to get a head=p_{head}=\frac{1}{2}

Probability to get a 4 in the die=p_{4}=\frac{1}{6}

Probability to get a head and get a 4 in die=[p_{1}tex]p_{head}\times p_{4}[/tex]=\frac{1}{2}\times \frac{1}{6} =\frac{1}{12}

Probability to get a tail=p_{tail}=\frac{1}{2}

Probability to get a heart=p_{heart}=\frac{13}{52} =\frac{1}{4}

Probability to get a tail and get a heart in the deck=p_{tail} \times p_{heart}=\frac{1}{2}\times \frac{1}{4}=\frac{1}{8}

Total probability to win a jackpot=p_{1}+p_{2}=\frac{1}{12}+\frac{1}{8}=\frac{5}{24}

So,probability to win a jackpot is \frac{5}{24}

3 0
3 years ago
Caterers made 272 cups of punch for a party. They will distribute the punch equally into 6 bowls. How many cups of punch will ea
motikmotik

Answer:

45.33 cups.

Step-by-step explanation:

272 divided by 6 gives this answer

8 0
2 years ago
Hiy im in kindergaten and i ned help on my homwwork wat is 5pluss7
inessss [21]

Step-by-step explanation:

5 + 7 = 12 \\

3 0
3 years ago
Read 2 more answers
PLEASE HELP ME WITH THIS MATH PROBLEM
pychu [463]

Answer:

A'(-1, -1)

Step-by-step explanation:

Dilation about the origin multiplies each individual coordinate value by the dilation factor.

A' = (1/3)A = (1/3)(-3, -3) = (-1, -1)

8 0
3 years ago
Read 2 more answers
G(t) = 3t + 4; Find g(−3)
Bess [88]
G(-3)= 3(-3)+4

g(-3) = -5
7 0
3 years ago
Other questions:
  • The absolute value of a number can be positive or negative.
    9·1 answer
  • PLEASE HELP!! ISSA DUMB KID!
    14·1 answer
  • What is 4263 - 1613 equal
    9·2 answers
  • How would you work this out ?
    8·1 answer
  • Simplify s^2-2s/ s^2 +3s-10 \ s-5/s+5
    14·1 answer
  • Evaluate each function at the given value.<br><br>f(x)=10x2x at x=4
    11·2 answers
  • Refer to the accompanying data​ table, which shows the amounts of nicotine​ (mg per​ cigarette) in​ king-size cigarettes,​ 100-m
    9·2 answers
  • Given m//n find the value of x. see attachment.
    13·1 answer
  • Please help me.
    15·1 answer
  • Tell whether the given value is a solution of the inequality.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!