Question

Will medall. In comments.

Answer 1

You know that for any [Image], neither sin[Image] nor cos[Image] can be greater than 1. How can you explain this using the unit circle definitions of sine and cosine? How can you explain it using the right triangle definitions of sine and cosine? As a follow-up question, consider why it is important to have both the right triangle definitions of sine and cosine and the unit circle definitions of sine and cosine. Can you give examples of situations that might be modeled with trigonometric functions? That is, can you give examples of phenomena that take on a series of values over and over again?

Answer 2

what are the images

Answer 3

i think it's supposed to be the theta sign

Answer 4

@KAIDEEKARMA

Answer 5

yeah the sin and cos functions oscillate between y=+1 and y=-1,

on the unit circle, any point on the circle has coordinates (x,y) = (cos(x) , sin(x)),
the radius is 1, so the largest x or y value you can manage on this thing is 1

Answer 6

since the radius is 1, and that is used as the hypotenuse value for sin and cos

sine is opp/hyp, so that will be the Y value distance , sin(x) = Y/ 1 = Y

cos is x value distance

Answer 7

In a right Triangle, the Sin and Cos are defined as a side length over the hypotenuse

the hypotenuse is the largest side in the triangle, therefore

sin(angle)=opposite /hypotenuse


hypotenuse is the largest, so sine is a fraction less than 1

Answer 8

could you do me a favor and number the question(s) you're answering pleasee.

like..

You know that for any [Image], neither sin[Image] nor cos[Image] can be greater than 1.
1. How can you explain this using the unit circle definitions of sine and cosine?

2.How can you explain it using the right triangle definitions of sine and cosine?

3.As a follow-up question, consider why it is important to have both the right triangle definitions of sine and cosine and the unit circle definitions of sine and cosine.

4. Can you give examples of situations that might be modeled with trigonometric functions?

5. That is, can you give examples of phenomena that take on a series of values over and over again?

Answer 9

just so i better understand what youre saying.. does that make sense? :( pleaseeee and thank you @DanJS

Answer 10

@DanJS

Answer 11

on the unit circle, the radius is 1, and each point on the circle is
(x,y) = ( cos(angle), sin(angole)), so from that i guess you can say the range of values for any x and y on that cirlce is -1 to 1

Answer 12

, the hypotenuse in a right triangle is defined to be the largest side

the sin(a) = opposite side / hypotenuse, since hypotenuse is larger, that will always be a fraction less than 1

Answer 13

you can see on the unit circle also, the +x axis intercept is cos(0) = 1, sme for +y axis, that is sin(90) = 1

Answer 14

@danjs would i just out that?