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____ [38]
3 years ago
5

Given tantheta = 4/3 and pi < theta < 3pi/2; find cos2theta

Mathematics
2 answers:
Sidana [21]3 years ago
8 0

Answer:

d. -7/25

Step-by-step explanation:

π<θ<3π/2  in third quadrant

tanθ = 4/3

sinθ = - 4/5

cosθ = - 3/5

cos 2θ = cos²θ - sin²θ = (- 3/5)² - (- 4/5)² = 9/25 - 16/25 = - 7/25

UkoKoshka [18]3 years ago
4 0

Answer:

-24/7

Step-by-step explanation:

We know that,  

tan

2

θ

=

2

tan

θ

1

−

tan

2

θ

.

∴

tan

2

θ

=

2

⋅

3

4

1

−

9

16

=

3

2

⋅

16

7

=

24

7

.

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alexira [117]

Answer:

<em>Test statistic </em>

<em>               </em>t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }  

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Step-by-step explanation:

<u><em>Step(i):-</em></u>

Given Mean of the Population (μ) = 8.0

<em>Mean of the sample (x⁻) = 8.25</em>

Given data

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Given sample size  n= 8

Given sample standard deviation(S) = 0.661

<u><em>Step(ii):-</em></u>

<em>Null hypothesis : H:  (μ) = 8.0</em>

<em>Alternative Hypothesis :H:(μ) > 8.0</em>

<em>Degrees of freedom = n-1 = 8-1=7</em>

<em>Test statistic </em>

<em>               </em>t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }<em></em>

<em>              </em>t = \frac{8.25 -8.0}{\frac{0.661}{\sqrt{8} } }<em></em>

<em>            t =  1.076</em>

<em>Critical value </em>

<em>                    t₍₇,₀.₀₅₎   = 2.3646</em>

<em>The calculated value   t =  1.076 < 2.3646 at 0.05 level of significance</em>

<em>Null hypothesis is accepted</em>

<em>Test the hypothesis that the true mean quiz score is 8.0 against the alternative that it is not greater than 8.0</em>

<em></em>

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d1i1m1o1n [39]
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Answer:

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