Question

For right ∆ABC with right ∠C, prove each of the following.

a. sin A < 1

b. cos A < 1

Answer 1

both sin and cos have maximum values at 1, what angles does that occure at for each

Answer 2

um sorry im not to sure

Answer 3

since the radius is 1, all the hypotenuse are 1, so sin(a) = y and cos(a) = x


each point on the circle (x , y) = (cos(a), sin(a))

Answer 4

i have to write a proof

Answer 5

start by stating givens , i havent done a formal one in awhile

Answer 6

try and get through it before doing the formal proof maybe

Answer 7

given sin A< 1

Answer 8

the given triangles are right

the sum of the 3 angles in a triangle are 180, so the angles A and B add to 90

Answer 9

the range of values for cos(a) and sin(a), are from -1 to 1

cos(0) = 1
cos(90) = -1, for example

Answer 10

ok

Answer 11

angles

A + B + C = 180, and C is said to be 90, so

A + B = 90

Answer 12

ok

Answer 13

we are talking about a distance, lengths of the sides, forget about the negative part on the domain of sin and cos, so

sin(a) < 1
cos(b) < 1

Answer 14

ok

Answer 15

that restricts all the angles to the first quadrant on that circle, and not including 90, or 0

Answer 16

to prove those, say A+B=90

so angles A and B must both be some value between 0 and 90, not including 0 or 90

Answer 17

ok thanks!!

Answer 18

then apply that to the definition of sin and cos

sin(0) = 0
sin(90 = 1

sin has to be less than 1

Answer 19

ok thanks

Answer 20

welcome, i think most of the ideas are there, just organize em,

Answer 21

ok i will thanks so mcuh

Answer 22

overall

the remaining unknown angles A and B have to total 90, so A can be 89.99999 and B the rest 0.00001 deg, and that works for example

that statement will tell you what the possible values for sin and cos will be

Answer 23

0 < A < 90
0 < B < 90

sin(0) < sin(A) < Sin(90)
0 < sin (A) < 1

Answer 24

sme for cos(A)

0 < A < 90

sin(0) < sin ( A) < sin(90)
0 < sin (A) < 1

Answer 25

the hard part is remembering all the 'official' names for properties and stuff for the reasons