The three identities below are all called pythagorean identities. the second and third follow from the first, as you
saw in example 1 and the exit ticket.
a. for which values of θ are each of these identities defined?
i. sin2(theta) + cos2(theta) = 1, where the functions on both sides are defined.
ii. tan2(theta) + 1 = sec2(theta), where the functions on both sides are defined.
iii. 1 + cot2(theta) = csc2(theta), where the functions on both sides are defined.
b. for which of the three identities is 0 in the domain of validity?
c. for which of the three identities is

2 in the domain of validity?
d. for which of the three identities is −
4 in the domain of validity?

Acell phone company offers two plans to its subscribers. at the time new subscribers sign up, they are asked to provide some demographic information. the mean yearly income for a sample of 40 subscribers to plan a is $45,000 with a standard deviation of $9,200. for a sample of 25 subscribers to plan b, the mean income is $64,300 with a standard deviation of $7,100. at the 0.025 significance level, is it reasonable to conclude the mean income of those selecting plan b is larger? assume unequal population standard deviations. hint: for the calculations, assume the plan a as the first sample. what is the decision rule? (negative amount should be indicated by a minus sign. round your answer to 3 decimal places.) compute the value of the test statistic. (negative amount should be indicated by a minus sign. round your answer to 2 decimal places.) what is your decision regarding h0 ? reject h0 fail to reject h0 compute the p-value. less than 0.01 between 0.01 and 0.025 between 0.025 and 0.05 between 0.05 and 0.10 greater than 0.10