Let's work on the left side first. And remember that
the<u> tangent</u> is the same as <u>sin/cos</u>.
sin(a) cos(a) tan(a)
Substitute for the tangent:
[ sin(a) cos(a) ] [ sin(a)/cos(a) ]
Cancel the cos(a) from the top and bottom, and you're left with
[ sin(a) ] . . . . . [ sin(a) ] which is [ <u>sin²(a)</u> ] That's the <u>left side</u>.
Now, work on the right side:
[ 1 - cos(a) ] [ 1 + cos(a) ]
Multiply that all out, using FOIL:
[ 1 + cos(a) - cos(a) - cos²(a) ]
= [ <u>1 - cos²(a)</u> ] That's the <u>right side</u>.
Do you remember that for any angle, sin²(b) + cos²(b) = 1 ?
Subtract cos²(b) from each side, and you have sin²(b) = 1 - cos²(b) for any angle.
So, on the <u>right side</u>, you could write [ <u>sin²(a)</u> ] .
Now look back about 9 lines, and compare that to the result we got for the <u>left side</u> .
They look quite similar. In fact, they're identical. And so the identity is proven.
Whew !
Answer:
=39.42857143 miles per hour
Step-by-step explanation:
To find the average speed, we need to the total distance and the total time
Distance 1
45 miles for 2 hours
45*2 = 90 miles
Distance 2
90 minutes * 1 hour/60 minutes = 1.5 hours
32 miles * 1.5 hours =48 miles
The total distance = 90+48 = 138 miles
The total time = 2 +1.5 = 3.5 hour
The average speed = total distance/ total time
= 138/3.5
=39.42857143 miles per hour
Answer:
Step-by-step explanation:
You could talk about how how or low it goes.
For instance: if the graph was going very high then suddenly low you could say that it was going very high until it suddenly dropped.
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Answer:
Statement 1. P
Reason 1. Theorem: The measure of an external angle of a triangle is equal to the sum of the measures of the remote interior angles.
Statement 2. 132 = 3x + 54
Statement 3. x = 26
A. It is an experiment as the sales director is applying treatment ( the training ) to a group and recording the results.
B. I would have 250 sales representatives from each region take the training and 250 from each region to not take it so i can be able to see if it affects both regions differently. The representatives from each region would be chosen at random and the length of their training would be the same for all.
C. now you would only be able to have 200 people from each region train. this would lower the percentage of the impact the training had on the amount of sales ( if any) . For example, if the original 250 trained people in a region increased the sales in that region by 20 percent and 50 of those people ended up not actually training, the sales would have only increased by 16 percent.
D. correlational research is best to establish causality. for example, the amount of training the representatives got may affect how much they are able to sell. also the number of representatives trained may affect the amount sold