Question

True or False:
1. the tangent increases in the third quadrant
2. the cosecant increases in the third and fourth quadrant
3. the sine increases in the third quadrant
4. the sine function is odd
5. the secant function is odd
6. in the first quadrant all six functions are positive
7. the sin 20 is less than the sin 25
8. the tan 45 is 1
9. the tangent is positive in the third and fourth quadrant
10. the tan 24 is less than tan 35
11. the greatest value of secant is 1
12. the cotangent function is odd
13. if the tangent is negative then the cotangent is negative

Answer 1

@Hero

Answer 2

@jim_thompson5910

Answer 3

thanks?

Answer 4

http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf

Answer 5

Many of these can be reasoned through with the help of a unit circle.

Answer 6

here is the unit circle

Answer 7

Quadrant III is in the lower left corner

Answer 8

i dont get the ones that talk about sin cos tan increasing and decreasing?? :\ ...i know the unit circle and the quadrants

Answer 9

as the angle increases,

a) sine increases

or

b) sine decreases

Answer 10

b?

Answer 11

yes, since tan = sin/cos, tangent also decreases in Q3

Answer 12

wait but can you explain how exactly the sin decreases?

Answer 13

oh wait, i'm not counting cosine here

as the angle increases, cosine also decreases in Q3

Answer 14

Also useful: http://www.sparknotes.com/math/trigonometry/graphs/section2.rhtml

Answer 15

oops cosine increases here i meant

Answer 16

how exactly do they "increase/decrease" ??

Answer 17

here is one angle

Answer 18

here is the tangent of that angle

Answer 19

increase the angle to get this new angle

Answer 20

the tangent of that angle is

Answer 21

you can see that the lengths of the tangent segments are getting longer, which means that tangent is increasing as the angle increases in Q3

Answer 22

no in Q2, sine is decreasing

Answer 23

same with Q3

Answer 24

how?

Answer 25

sine is just the y coordinate of the point on the unit circle

Answer 26

okay i know
tan=slope
sin=y
cos=x

Answer 27

in Q2 and Q3, the y coordinates are decreasing

Answer 28

no, the x coordinates are decreasing..?

Answer 29

yeah and tan = length of tangent segment that starts at the terminal point and it intersects the x axis

Answer 30

in Q2, the x coordinates decrease,

in Q3, the x coordinates increase

Answer 31

right?

Answer 32

right