# MTH1014 Quiz 8Spring 2013

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This is quiz 8 to be taken by Friday, 19 April 2013. It should take you between half an hour and 2 hours to answer the following questions. You should do this quiz after doing the rest of assignment 8'.

Note that each of the inverse trigonometric functions has 4 names:
sin-1(theta) = arcsine(theta) = arcsin(theta) = asin(theta)
cos-1(theta) = arccosine(theta) = arccos(theta) = acos(theta)
tan-1(theta) = arctangent(theta) = arctan(theta) = atan(theta)
csc-1(theta) = arccosecant(theta) = arccsc(theta) = acsc(theta)
sec-1(theta) = arcsecant(theta) = arcsec(theta) = asec(theta)
cot-1(theta) = arccotangent(theta) = arccot(theta) = acot(theta)

We will use the third form here. You may use any of the four forms.

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Please answer the following questions on this form (or on a paper copy of this form).

1. Carefully define the functions arcsin(theta) and arccos(theta). State the domain, range and intercepts of these functons.

2. Carefully define the function arctan(theta). State the domain, range and intercepts of this functon.

3. Carefully define the functions arccsc(theta) and arcsec(theta). State the domain, range and intercepts of these functons.

4. Carefully define the function arccot(theta). State the domain, range and intercepts of this functon.

5. Compute the exact value of sin(theta/3)*sin(theta/3)+cos(theta/3)*cos(theta/3). Show your work, but there will be no credit for anything other than an exact answer.

6. Carefully give the sum and difference formulae for the sine, cosine and tangent functions.

7. Carefully give the double-angle and half-angle formulae for the sine, cosine and tangent functions. Give the square root using the sqrt function, not the radical sign.

8. Carefully give the sum to product formulae for the sine and cosine formulae.

9. Carefully solve sin(theta)+cos(theta) = sqrt(3/2), as accurately as you can. Show your work.

10. Carefully solve tan(5*theta)+cot(5*theta)=2, as accurately as you can. Show your work.

11. Carefully solve cos(7*theta)-tan(7*theta)=sqrt(3)/6, as accurately as you can. Show your work.

12. As a special reward for students who are trying to stay current on the work for the course, this question is worth 1 full quiz of extra credit if turned in by the due date of this quiz, but only normal one question credit if turned in later. Carefully solve cos(3*theta)*cos(3*theta) = 1+sqrt(3)/2, as accurately as you can. Show your work.

<==== Do this AFTER you''ve answered all the questions

You probably DON'T want to do this ===>

Revised 11 April 2013