Trigonometry Review (Ch. 7)

The Unit Circle

100

1) What is sin(3pi/2)? 

-1

200

17) Find cos^-1(-1/2) on the interval [0, pi].

2pi/3

300

20) What is tan(pi/6)?

Square root of 3 over 3

400

11) What is cot(2pi)?

Undefined

500

8) What is sec²(7pi/4)?

2

7.1 (Trig Identities & Expressions)

100

21) Simplify to a number or to one trig. function

sec(x)cos(x)

1

200

2) Simplify to one number or to one trig. function.

tan(x)/sec(x)

sin(x)

300

14) Simplify to a number or one trig. function. 

sin(x)tan(x)cot(x)csc(x)

1

400

18) Simplify to a number or one trig. function.

tan²(x)csc²(x)

sec²(x)

500

4) Simplify to a number or to one trig. function. 

sec(x)-sin(x)tan(x)

cos(x) 

7.2 (Sum & Difference Formulas)

100

22) Is this the sum or difference formula for cosine? 

cos(a)cos(b)-sin(a)sin(b)

Sum Formula

200

12) What is this the formula for? 

sin(a)cos(b)-cos(a)sin(b)

Difference formula for sine. 

300

3) Use the sum or difference formula to find the exact value of sin(105^o).

(square root of 6 + square root of 2) over 4

400

Free Points!! YAY

Woohoo!!

500

7) Find the exact value of tan(435^o) by using a sum formula.

(square root of 3 + 3) over (3 - square root of 3)

7.3 (Double-Angle & Half-Angle Formulas)

100

9) This is the double-angle formula for which trig function? 2sin(x)cos(x)

sin(2x)

200

6) If the angle x is in quadrant 1, and I am finding the sin(x/2), will my answer be positive or negative? 

Positive

300

Uh oh....Lost some points...

Oh man... :(

400

13) If tan(x)=3/4 and x is in quadrant 1, what is sin(2x)? 

24/25

500

16) If tan(x)= -2 and x is in quadrant 4, what is cos(x/2)?

-square root ((5 + square root(5))/10)

7.5 (Solving Trig. Equations)

100

23) Give one solution of the equation sin(x)= -1/2

7pi/6 or 11pi/6

200

19) Solve for x on the interval [0, 2pi)

cos(x) + square root of 3 = -cos(x)

Hint (2 solutions)

5pi/6 and 7pi/6

300

10) Solve for x on the interval [0, 2pi)

4sin²(x) - 3 = 0

(hint: 4 solutions)

pi/3, 2pi/3, 4pi/3, and 5pi/3

400

15) Solve for x on the interval [0, 2pi)

2sin(x)cos(x) + cos(x) = 0

pi/2, 3pi/2, 7pi/6, and 11pi/6

500

5) Solve for x on the interval [0, 2pi)

2sin²(x) + 2sin(x) - 1 = 0

pi/6, 5pi/6, 3pi/2