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BARSIC [14]
2 years ago
14

1.1 solve for x, where 0°< x 90°. write your answer to one decimal place. 1.1.1 tanx=sin38° 1.1.2cosec( x+10°)=1.345​

Mathematics
1 answer:
snow_lady [41]2 years ago
5 0

The value of x in tan(x)=sin38° is 31.6 and the value of x in cosec(x+10°)=1.345​ is 38.0

<h3>How to solve the trigonometry ratios?</h3>

The equations are given as:

tan(x)=sin38°

cosec( x+10°)=1.345​

In tan(x)=sin38°, we have:

tan(x)=0.6157

Take the arc tan of both sides

x = 31.6

Also, we have:

cosec(x+10°)=1.345​

Take the inverse of both sides

sin(x+10°) = 0.7434

Take the arc sin of both sides

x+10 = 48.0

Subtract 10 from both sides

x = 38.0

Hence, the value of x in tan(x)=sin38° is 31.6 and the value of x in cosec(x+10°)=1.345​ is 38.0

Read more about trigonometry ratios at:

brainly.com/question/11967894

#SPJ1

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Ber [7]
The problem statement tells you ∠MLK is 61°, so ∠LMK = 180° -68° -61° = 51°. Since a tangent is always perpendicular to a radius, triangles LJM and LJK are right triangles.

Trigonometry tells you ...
  tangent = opposite / adjacent
so you can write two relations involving LJ.
  tan(51°) = LJ/JM
  tan(68°) = LJ/JK
The second equation can be used to write an expression for LJ that can be substituted into the first equation.
  LJ = JK*tan(68°) = 3*tan(68°)
Substituting, we have
  tan(51°) = 3*tan(68°)/JM
Multiplying by JM/tan(51°), we get
  JM = 3*tan(68°)/tan(51°)
  JM ≈ 6.01

The radius of circle M is about 6.01.

6 0
3 years ago
If sin theta equals 12 divided by 13 and theta is in quadrant 2 cos20 equals? and cos theta equals?
Anni [7]

Answers:

  • cos(2theta) = -119/169
  • cos(theta) = -5/13

=====================================================

The given info is:

  • sin(theta) = 12/13
  • theta is in quadrant II

From that, we can use the pythagorean trig identity to find that cos(theta) = -5/13. Keep in mind that cosine is negative in quadrant II.

Now use the trig identity below to compute cos(2theta)

\cos(2\theta) = \cos^2(\theta)-\sin^2(\theta)\\\\\cos(2\theta) = \left(\frac{-5}{13}\right)^2-\left(\frac{12}{13}\right)^2\\\\\cos(2\theta) = \frac{25}{169}-\frac{144}{169}\\\\\cos(2\theta) = \frac{25-144}{169}\\\\\cos(2\theta) = -\frac{119}{169}\\\\

Other options you could use are these identities

\cos(2\theta) = 2\cos^2(\theta)-1\\\\

or

\cos(2\theta) = 1-2\sin^2(\theta)\\\\

3 0
3 years ago
F(x)=-x^2+19<br><br> Find f(3)
Arturiano [62]

Answer:

f(3) = 10

Step-by-step explanation:

f(x)=-x^2+19

Let x= 3

f(x)=- (3)^2+19

    = -9 + 19

    = 10

8 0
3 years ago
Read 2 more answers
Some parts of California are particularly earthquake-prone. Suppose that in one metropolitan area, 32% of all homeowners are ins
Bumek [7]

Answer:

P(X = 0) = 0.2138

P(X = 1) = 0.4025

P(X = 2) = 0.2841

P(X = 3) = 0.0891

P(X = 4) = 0.0105

Step-by-step explanation:

For each homeowner, there are only two possible outcomes. Either they have invested in earthquake insurance, or they have not. The probability of a home owner having invested in earthquake insurance is independent from other homeowners. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

32% of all homeowners are insured against earthquake damage.

This means that p = 0.32

Four homeowners are to be selected at random.

This means that n = 4

Find the probability distribution of X.

This is the probability of each outcome

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{4,0}.(0.32)^{0}.(0.68)^{4} = 0.2138

P(X = 1) = C_{4,1}.(0.32)^{1}.(0.68)^{3} = 0.4025

P(X = 2) = C_{4,2}.(0.32)^{2}.(0.68)^{2} = 0.2841

P(X = 3) = C_{4,3}.(0.32)^{3}.(0.68)^{1} = 0.0891

P(X = 4) = C_{4,4}.(0.32)^{4}.(0.68)^{0} = 0.0105

6 0
3 years ago
14 - (2x + 5) = -2x +9<br> How do you solve this problem?
Alex_Xolod [135]

Answer:

x ∈ R (all reals)

Step-by-step explanation:

14 - (2x + 5) = -2x + 9

Take out parentheses

14 - 2x - 5 = -2x + 9

Simplify

9 = 9

<em>Since 9 does equal 9, it means that this equation can be true for all real values of x.</em>

5 0
4 years ago
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