Given: Cosine (x minus y)
1 answer:
The required steps that complete the proof are:
Step 1: Cofunction Identity
Step 5: Sine Difference Identity
Step 6: Cofunction Identity
Step 7: Cosine Function Is Even, Sine Function Is Odd
<h3>Trigonometry identity</h3>Given the cosine function expressed as:
- cos(x - y)
The first step is to apply the cofunction identity as shown:
- Step 1: Cofunction Identity
cos(90 - x) = sin x
cos(x - y) = sin (90-(x-y))
- Step 5: Sine Difference Identity
For the fifth step, you will apply the sine difference identity.
- Step 6: Cofunction Identity
To get the sixth step, you will apply the Cofunction Identity on the result in the fifth step.
The final step 7 will be
- Step 7: Cosine Function Is Even, Sine Function Is Odd
Learn more on trigonometry identity here: brainly.com/question/24496175
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Answer:
There is enough evidence to support the claim that there is a significant difference in the proportion of residents and commuters who prefer the switch.
Step-by-step explanation:
This is a hypothesis test for the difference between proportions.
The claim is that there is a significant difference in the proportion of residents and commuters who prefer the switch.
Then, the null and alternative hypothesis are:
The significance level is 0.05.
The sample 1 (residents), of size n1=200 has a proportion of p1=0.4.
The sample 2 (conmuters), of size n2=200 has a proportion of p2=0.6.
The difference between proportions is (p1-p2)=-0.2.
The pooled proportion, needed to calculate the standard error, is:
The estimated standard error of the difference between means is computed using the formula:
Then, we can calculate the z-statistic as:
This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):
As the P-value (0.00008) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that there is a significant difference in the proportion of residents and commuters who prefer the switch.