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4 years ago

If sin theta + cos theta = root2, then evaluate tan theta + cot theta

2 answers:

8 0

$\displaystyle\\\\\sin\theta+\cos\theta= \sqrt{2}\\\\\sin\theta+\cos\theta= 2\times\frac{\sqrt{2}}{2}\\\\\implies~~\sin\theta=\cos\theta= \frac{\sqrt{2}}{2}\\\\\implies~~\theta=45^o\\\\\implies~~\tan\theta + \cot\theta=\tan45^o + \cot45^o=1+1=\boxed{\bf2}$

ella [17]4 years ago

7 0

sin theta + cos theta = root2

Squaring both sides:

(sin theta + cos theta)^2 = 2

sin^2 theta + cos^2 theta + 2 sin theta cos theta = 2

1 + sin 2theta = 2

sin 2theta = 1

2 theta = 90

theta = 45

so tan theta + cot theta = 1 + 1

= 2

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3 years ago

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4 years ago

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No, there is no strong evidence that the percentage of the fleet out of compliance is different from their initial thought.

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The company initially believed that 30% of the fleet was out of compliance.

Let p = percentage of the fleet that was out of compliance.

SO, Null Hypothesis, $H_0$ : p = 30% {means that the percentage of the fleet out of compliance is same as their initial thought}

Alternate Hypothesis, $H_A$ : p $\neq$ 30% {means that the percentage of the fleet out of compliance is different from their initial thought}

The test statistics that will be used here is One-sample z proportion statistics;

T.S. = $\frac{\hat p-p}{{\sqrt{\frac{\hat p(1-\hat p)}{n} } } } }$ ~ N(0,1)

where, $\hat p$ = percentage of the fleet out of compliance = $\frac{4}{25}$ = 16%

n = sample of systems tested = 25

So, test statistics = $\frac{0.16-0.30}{{\sqrt{\frac{0.16(1-0.16)}{25} } } } }$

= -1.909

The value of the test statistics is -1.909.

Since in the question we are not given with the level of significance at which hypothesis can be tested, so we assume it to be 5%. Now at 5% significance level, the z table gives critical values between -1.96 and 1.96 for two-tailed test.

Since our test statistics lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the percentage of the fleet out of compliance is same as their initial thought.

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