# math

math. Hw3-5

A circular sector has radius r=3.7 and central angle θ=110∘. Determine:

Arclength = .

Area = .

Hw 4-1

2,0,3,1; 0,2,1,3

Without a calculator, match each of the equations below to one of the graphs by placing the corresponding letter of the equation under the appropriate graph.

A. y=sin(2t) B. y=sin(t+2) C. y=2sin(t) D. y=sin(t)+2    1. 2. 3. 4.

4-2

State the period, amplitude, phase shift, and horizontal shift of the following function:

y=−2sin(2t+π/3)

(a) The period of the graph is (give an exact answer) (b) The amplitude of the graph is (give an exact answer) (c) The phase shift of the graph is (give an exact answer) (d) The horizontal shift of the graph is (give an exact answer) (e) Based on your answers above, without a calculator sketch the graph of the function above over the interval −πt≤2π.

4-3

Decide whether the following graph appears to be a periodic function. If so enter the value of its period in the blank. If the graph does not appear to be periodic enter NONE.

The period is (Enter NONE if not periodic.) help (numbers) 4-4

Decide whether the following graph appears to be a periodic function. If so enter the value of its period in the blank. If the graph does not appear to be periodic enter NONE.

The period is (Enter NONE if not periodic.) help (numbers) 4-5

 Assume that sin(A)=sin(B) in the figure. Find exact answers for each of the values below, not decimal approximations. All angles are given in radians, and your answers should be in radians. (a) If A=π/5, then B=  help (numbers) (b) If A=1.2, then B=  help (numbers) 4-6

Match each of the letters A-G in the figure to one of the following values of x (in radians): 1,2,4,5,π/2,π, and 3π/2.

 x = 1 2 4 5 π/2 π 3π/2 Letter 4-7

Find a possible formula for the trigonometric function graphed below. Use x as the independent variable in your formula.

f(x)= help (formulas) 4-8

Find a formula for the trigonometric function graphed below. Use x as the independent variable in your formula.

f(x)= help (formulas) 4-9

Below is the graph of the function f(x)=10sin(π5/x) in blue, and a second sinusoidal function y=g(x) in red, which is a horizontal shift of y=f(x). Find a formula for the function g(x). g(x)= help (formulas) 4-11

Find the equation of a cosine curve that is obtained by shifting the graph of y=cos(x) – to the left 1 units and – upward 3 units and – vertically compressed by a factor of 7 and – vertically flipped

y=

4-12

Using sum or difference formulas, find the exact value of sin(285∘). Express your answer in the form sin(285∘)=−a√(b√+1)/4 for some numbers a and b.

ab=

4-13

Using sum or difference formulas, find the exact value of cos(105∘). Express your answer in the form cos(105∘)=a√(1−b√)/4 for some numbers a and b.

ab=

4-15

Use the sum formula to fill in the blanks in the identity below. Note: Give exact answers. Do not use decimals. Your answer should be a fraction or an integer. If the answer requires a square root enter it as sqrt . E.g. the square root of two should be entered as sqrt(2).

sin(x+π/4)= sin(x) + cos(x)

4-16

Use an addition or subtraction formula to write the expression as a trigonometric function of one number: cos3π/7 cos2π/21+sin3π/7 sin2π/21 =cosπ/A=B/2. A= , B= .

4-17

If sin2x−cos2x=2√sin(2x+), then the number 0<A= <2.

4-17

If sin(xπ)=Asin x, then A= .

4-18

Given cos(α)=55√/8 and α is in quadrant IV and cos(β)=−13√/7 and β is in quadrant II. Use sum and difference formulas to find the following: Note: You are not allowed to use decimals in your answer.

sin(α+β)=

5-1

Using sum or difference formulas, find the exact value of sin(255∘). Express your answer in the form sin(255∘)=−a√(b√+1)/4 for some numbers a and b.

ab=

5-2

Using sum or difference formulas, find the exact value of cos(255∘). Express your answer in the form cos(255∘)=a√(1−b√)/4 for some numbers a and b.

ab=

5-3

Use C to denote cosx, and express cos(x+20,000π)= in terms of C. Similarly, express cos(x+20,001π)= in terms of C.

5-4

Use a sum or difference formula or a half angle formula to determine the value of the trigonometric functions. Give exact answers. Do not use decimal numbers. The answer should be a fraction or an arithmetic expression. If the answer involves a square root it should be enter as sqrt; e.g. the square root of 2 should be written as sqrt(2); sin(π/12) = sin(π/8)= cos(5π/12)= cos(7π/12)=

5-5

Use the sum formula to fill in the blanks in the identity below. Note: Give exact answers. Do not use decimals. Your answer should be a fraction or an integer. If the answer requires a square root enter it as sqrt . E.g. the square root of two should be entered as sqrt(2).

sin(x+π/3)= sin(x) + cos(x)

5-6

Use an addition or subtraction formula to write the expression as a trigonometric function of one number: cos3π/7cos2π/21+sin3π/7sin2π/21=cosπ/A=B/2. A= , B= .

5-7

If sin(xπ)=Asinx, then A= .

5-8

Use an addition or subtraction formula to simplify the expression: tan(π/2−u)=cot(f(u)). f(u)= .

5-9

Given cos(α)=−65√/9 and α is in quadrant II and sin(β)=−6/7 and β is in quadrant III. Use sum and difference formulas to find the following: Note: You are not allowed to use decimals in your answer.

sin(α+β)=

7.1034

math

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