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Geometry and Trig Questions

Set 1
11: The actual definition of the word tangent comes from the Latin word tangere, meaning "to touch" in mathematics the tangent line touches the graph at a circle at only one point and function values of tan ѳ are obtained from the length of the line segment tangent to a unit circle. Can the line segment ever be greater than 1700 units long?
12: Use the information given to write a sinusoidal and sketch it's graph, then choose the appropriate equation and graph below. Max 160; min20: P=90?
13: In Vancouver British Columbia the number of hours of daylight reaches a low of 7.4hrs in January, and a high of nearly 14.1 hr in july. Find a sinusoidal equation model for the number of daylight hours each month. Assume t=0 corresponds to January 1st round final and intermediate answers to one decimal place if necessary.
14: Identify the amplitude (A), Period (P), horizontal shift (HS), Verticle shifts (VS), and end points of the primary interval (PI) for each function given. Y=284sin(pi/12t + 4pi/3)+226
15: Find the sinusoidal equation for the information given. If nessecary round calculations to the nearest hundredth. Minimum value at ( 6,8280); max value at (22,23126); period 32year.
Set 2
1: Fill in the blank with the appropriate word or phrase. Two fundamental reciprocal identities are: sin ѳ=1/? And cos ѳ=1/?
2: Verify the equation is an identity using factoring and fundamental identities. Tan^2 x csc^2 x -tan ^2 x =1. Is this equation an identity?
3: write the given function entirely in terms of the second function indication. Sec x in terms of tan x.
4: Is this equation an identity? ?
5: writing a given expression in an alternative form is an idea used at all levels of mathematics. In future classes, it is often helpful to decompose a power into smaller powers (as in writing A^3 as A*A^2) or to write an expression using known identities so it can be factored. Can 6sin^2 x cos x - x be factored into (1-cos x )(1+cos x )(6cos x - )?
6: Is this equation an identity?
7: Is this equation an identity? =cos x
8: Is this equation an identity? (csc x +cot x )^2=
9: Fill in each blank with the appropriate word or phrase. Two fundamental Pythagorean identities are? Sin^2 ѳ +?^2=1 and 1+?^2=csc^2 ѳ
10: Find the exact value of the given expression? Cos( ) cos( -sin( sin(
11: Rewrite as a single expression. Sin ( ) cos ( + cos ( ) sin (
12: Find the exact value of the expression using a sum or difference identities. Sin 135⁰
13: Given a and B are acute angles with cos a= and sec B= , find sin (a+B)?
14: Is this equation an identity? Cos (a+B) + cos (a-B) =-2 cos a cos B?
15: Find exact values for sin (20), cos (20), and tan (20) using the information given. Cot (ѳ) = - ; ѳ in QII

Attachments

Solution Preview

For SET 1, we'll use the formula:
Sinusoidal Function:

|A| = amplitude
B = cycles from 0 to
period =
D = vertical shift (or displacement)
C = horizontal shift (phase shift)

Set 1
11: The actual definition of the word tangent comes from the Latin word tangere, meaning "to touch" in
mathematics the tangent line touches the graph at a circle at only one point and function values of tan ѳ
are obtained from the length of the line segment tangent to a unit circle. Can the line segment ever be
greater than 1700 units long?

As the angle x comes close to 90 degrees , the length of the tangent line goes to infinity, so YES , it is possible that the tangent line is greater than 1700 units.

12: Use the information given to write a sinusoidal and sketch it's graph, then choose the appropriate
equation and graph below. Max 160; min20: P=90?

Amplitude = (Max-min)/2 = 160-20 / 2 = 140/2= 70
Vertical shift is 90 ( 70+20)
Period = 360 ( or 2Pi) so argument should be x/4 since P= 90 = 360/4
Therefore the equation is: 70sin(x/4) + 90

13: In Vancouver British Columbia the number of hours of daylight reaches a low of 7.4hrs in January,
and a high of nearly 14.1 hr in july. Find a sinusoidal equation model for the number of daylight hours
each month. Assume t=0 corresponds to January 1st round final and intermediate answers to one
decimal place if necessary.

Same as previous problem.
We have min = 7.4
Max = 14.1
Period P = 6 ( months). Now we graph:

14: Identify the amplitude (A), Period (P), horizontal shift (HS), ...

Solution Summary

This solution is comprised of a detailed explanation to answer Geometry Questions.

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