Trigonometry

Question 1

What are sine, cosine and tangent when x=0?

Answer 1

Sine: 0
Cosine: 1
Tangent: 0

Question 2

What are the exact values of sine, cosine and tangent when x=30?

Answer 2

Sine: 1/2
Cosine: square root 3/2
Tangent: square root 3/3

Question 3

What is the exact values of sine, cosine and tangent when x=60?

Answer 3

Sine: square root 3/2
Cosine: 1/2
Tangent: square root 3

Question 4

What is the exact value of sine, cosine and tangent when x=45?

Answer 4

Sine: square root 2/2
Cosine: square root 2/2
Tangent: 1

Question 5

What is the exact values of sine, cosine and tangent when x=90?

Answer 5

Sine: 1
Cosine: 0
Tangent: Undefined

Question 6

What is the formula for converting degrees to radians?

Answer 6

(180x)/Pi

Question 7

What is the formula for converting radians to degrees?

Answer 7

(Pi x)/180

Question 8

What are a list of exact value degrees when converted to radians?

Answer 8

30 -> Pi/6
45 -> Pi/45
60 -> Pi/3
90 -> Pi/2
180 -> Pi
270 -> 3Pi/2
360 -> 2Pi

Question 9

Where is sine positive and negative?

Answer 9

Positive: Quadrant 1 & 2
Negative: Quadrant 3 & 4

Question 10

What quadrants is cosine negative and positive?

Answer 10

Positive: Quadrant 1 & 4
Negative: 2 & 3

Question 11

What quadrants is tangent positive and negative in?

Answer 11

Positive: 1 & 3
Negative: 2 & 4

Question 12

What is the Pythagorean identity?

Answer 12

sin^2(Ø)+cos^2(Ø)=1

Question 13

What is the tangent identity?

Answer 13

tan(Ø)=sin(Ø)/cos(Ø)

Question 14

What are the two similar complementary function identities?

Answer 14

sin(Pi/2-Ø)=cos(Ø)

cos(Pi/2-Ø)=sin(Ø)

Question 15

What are the steps to making a good sine or cosine graph?

Answer 15

1. Amplitude
2. Period
3. Mean position
4. Maximum
5. Minimum
6. X-intercepts?
7. Is the graph positive or negative?

Question 16

What is the template equation for sine, cosine and tangent?

Answer 16

y=a sin(bx)+c
y=a cos(bx)+c
y=a tan(bx)+c

Question 17

What is the pronumeral for amplitude?

Answer 17

a

Question 18

How do you find the period of a sine or cosine graph?

Answer 18

2 Pi/b

Question 19

What is the pronumeral for the mean position?

Answer 19

c

Question 20

What is the equation for the maximum and minimum?

Answer 20

Maximum: c+a
Minimum: c-a

Question 21

What is the equation for finding the x-intercepts for a cosine graph when c=0?

Answer 21

+ pi
- 2b
And then occurs every 1/2 period to the left or right of this

Question 22

How do you find the x intercepts of sine when c=0?

Answer 22

+ Pi
- b
And every 1/2 period to the left or right of this

Question 23

What are the steps to making a good tangent graph?

Answer 23

1. No amplitude
2. Period
3. X-intercepts (when c=0, this is the same as period)
4. Asymptotes
5. Mean position
6. It has a range of R

Question 24

What is the equation for finding a tangent period?

Answer 24

Pi/b

Question 25

How do you find the x-intercepts of a tangent graph when c=0?

Answer 25

X=Pi/b

This is the same as the period

Question 26

How do you find the asymptotes of a tangent graph?

Answer 26

Y=Pi/2b and -Pi/2b and every period to the left or right of those?

Question 27

What is the general solution for sine and cosine?

Answer 27

If sin(x)=a then x=2nPi+sin^-1(a)
If cos(x)=a then x=2nPi+ or -cos^-1(a)

Question 28

What needs to be determined when solving trigonometric equations?

Answer 28

1. The first quadrant angle, irrespective of the sign.
2. The two quadrants in which the sign is positive or negative.
3. Two solutions between x=0 and x=2Pi (use the appropriate sine, cosine or tangent symmetry property)
   If more solutions are required:
4. Repeatedly add or subtract the period to the two solutions as many times as required.
5. Stop when all solutions within in the domain are found.
6. If no domain is given, a general solution is required.