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Scilla [17]
3 years ago
13

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Complete the st

atements below, simplify all ratios and keep them as improper fractions. If cos(θ) = and sin(θ) is negative, then sin(θ) = and tan(θ) = .
Mathematics
1 answer:
Zina [86]3 years ago
5 0

Question:

If cos(θ) =-8/17 and sin(θ) is negative, then sin(θ) = ___  and tan(θ) =___.

Answer:

Sin\theta = \frac{-15}{17}

Tan\theta = \frac{15}{8}

Step-by-step explanation:

Given

cos(θ) =-8/17

Required

sin(θ) = __

tan(θ) =__

The first step is to determine the length of the third side

Given that

cos(\theta) = \frac{Adj}{Hyp}

Where Adj and Hyp represent Adjacent and Hypotenuse

cos(\theta) = \frac{-8}{17}

By comparison

Adj = -8\ and\ Hyp = 17

Using Pythagoras

Hyp^2 = Adj^2 + Opp^2

By Substitution

17^2 = (-8)^2 + Opp^2

289 = 64 + Opp^2

Subtract 64 from both sides

289 - 64 = 64 - 64 + Opp^2

225 = Opp^2

Take square roots of both sides

\sqrt{225} = \sqrt{Opp^2}

\sqrt{225} = Opp

15 = Opp

Opp = 15

The question says that sin(θ) is negative; This implies that θ is in the third quadrant and as such

Opp = -15

From trigonometry

Sin\theta = \frac{Opp}{Hyp}

Sin\theta = \frac{-15}{17}

Also from trigonometry

Tan\theta = Sin\theta / Cos\theta

Tan\theta = \frac{-15}{17} / \frac{-8}{17}

Tan\theta = \frac{-15}{17} * \frac{-17}{8}

Tan\theta = \frac{-15 * -17}{17  * 8}

Tan\theta = \frac{15 * 17}{17  * 8}

Tan\theta = \frac{15}{8}

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8 and 8/12 - 2 and 3/4. as a fraction ​
hjlf

Answer:

the answer is 71/12 or 5 and 11/12

Step-by-step explanation:

8x12= 96

96+8= 104

104/12= 8 8/12

2x4=8

8+3=11

11/4= 2 3/4

11/4 x 3/3= 33/12

104/12-33/12= 71/12 or 5 11/12

7 0
2 years ago
Use the unit circle to evaluate the followingHow do I solve this problem?
Ilya [14]

Notice that:

\cos (\frac{4\pi}{3})=\cos (\pi+\frac{\pi}{3})\text{.}

Recall that:

\cos (\pi+x)=-\cos (x)\text{.}

Therefore:

\cos (\frac{4\pi}{3})=-\cos (\frac{\pi}{3})=-\frac{1}{2}\text{.}

Answer:

cos(\frac{4\pi}{3})=-\frac{1}{2}\text{.}

6 0
1 year ago
When was geometric sequence discovered and who made it
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3 years ago
Priya bought these items at the grocery store. Find each unit price.
Xelga [282]

Answer:

1 roll of toilet paper would cost $50

Step-by-step explanation:

5 0
2 years ago
Which expressions are equivalent?
trapecia [35]

Only 3(a−b) and 3a−3b are equivalent

Further explanation:

We have to evaluate each expression to evaluate if the expressions are equivalent or not.

So,

<u>For 3(a−b)</u>

3(a-b)\\Distributing\ 3\ in\ bracket\\3.a-3.b\\=3a-3b

As we can see that 3(a-b) results in 3a-3b so these are equivalent

<u>For 2a(2+b)</u>

2a(2+b)\\Distributing\ 2a\\2a.2+2a.b\\=4a+2ab

As we can see that 2a(2+b) doesn't result in 4ab so these are not equivalent

Hence,

Only 3(a−b) and 3a−3b are equivalent

Keywords: Equivalent expression, Polynomials

Learn more about polynomials at:

  • brainly.com/question/4824362
  • brainly.com/question/4847829

#LearnwithBrainly

3 0
3 years ago
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