a Start by entering the function in our calculator. Push Y= and write the function on the first row by pushing sin followed by X,T,$θ$,n.
B
b To change the table setup, push 2nd and WINDOW and change the table.
C
c To change the table setup, push 2nd and WINDOW and change the table.
D
d Remember, the sine ratio is the ratio of the opposite side to the hypotenuse in a right triangle. What happens to the sine ratio when the opposite side becomes extremely long?
A
a 0.99985
B
b 1
C
cGreatest Value: 1 Close to 90^(∘): 0.9999 It does NOT contradict it.
D
d See solution.
Practice makes perfect
a Let's start by entering the function in our calculator. Push Y= and then write the function on the first row by pushing sin followed by X,T,θ,n.
To change the table setup, push 2nd and WINDOW and change the table start to 80 and the increments to 1. By pushing 2nd and GRAPH we get the table with the desired setup.
Finally, we will scroll down until we reach 89^(∘).
As we can see, sin89^(∘) equals 0.99985.
b Now we need to change the table setup again. Push 2nd and WINDOW and change the setup so that X starts at 89 and changes by increments of 0.1.
Next, we will scroll down to 89.9^(∘).
As we can see, sin89.9^(∘) equals 1 according to the calculator.
c Let's change the table interval to 0.01 and 0.001. to see what happens as we get closer to 90^(∘).
No matter how small we make the increments, the values of sinx stay at 1 as we get closer to 90^(∘).
d The definition of the sine ratio is the ratio of an angle's opposite side to the hypotenuse in a right triangle.
Let's show the sine ratio of a few angles in a right triangle.
As we can see, when the angle increases the sine ratio also increases. If we could draw a triangle where the hypotenuse and opposite leg to the reference angle were long enough, we would see that the sine ratio would approach 1.
