For his long distance phone service, Boris pays a $7 monthly fee plus 7 cents per minute. Last month, Boris's long distance bill
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Answer:
- sin θ ≈ -0.08667
- cos θ ≈ 0.99624
Step-by-step explanation:
Straightforward use of the inverse tangent function of a calculator will tell you θ ≈ -0.08678 radians. This is an angle in the 4th quadrant, where your restriction on θ places it. (To comply with the restriction, you would need to consider the angle value to be 2π-0.08678 radians. The trig values for this angle are the same as the trig values for -0.08678 radians.)
Likewise, straightforward use of the calculator to find the other function values gives ...
sin(-0.08678 radians) ≈ -0.08667
cos(-0.08678 radians) ≈ 0.99624
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<em>Note on inverse tangent</em>
Depending on the mode setting of your calculator, the arctan or tan⁻¹ function may give you a value in degrees, not radians. That doesn't matter for this problem. sin(arctan(-0.087)) is the same whether the angle is degrees or radians, as long as you don't change the mode in the middle of the computation.
We have shown radians in the above answer because the restriction on the angle is written in terms of radians.
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<em>Alternate solution</em>
The relationship between tan and sin and cos in the 4th quadrant is ...
That is, the cosine is positive, and the sign of the sine matches that of the tangent.
This more complicated computation gives the same result as above.
Using the confidence interval, it is found that the correct conclusion regarding the hypotheses test is given by:
Reject H0. There is convincing evidence that this individual’s true mean heart rate while working out differs from 150.
<h3>What are the hypotheses tested?</h3>At the null hypotheses, it is tested if the mean is of 150, that is:
At the alternative hypotheses, it is tested if the mean is different of 150, hence:
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The confidence interval is (158, 167). Since it does not contain 150, we reject the null hypotheses, hence the correct option is:
Reject H0. There is convincing evidence that this individual’s true mean heart rate while working out differs from 150.
More can be learned about confidence intervals at brainly.com/question/25890103
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