Trig Ratio Values Using Bow-Tie Diagram: sin 45, cos 60, tan 30, tan 45

[Imperil]

Use the "bow-tie" diagram to state the value of each trigonometric ratio.
a) sin 45
b) cos 60
c) tan 30
d) tan 45

My Answer:

a) 1 / [tex]\sqrt{2}[/tex]
b) 1 / 2
c) 1 / [tex]\sqrt{3}[/tex]
d) 1

Once again with this text the wording has thrown me off. It asks for the ratios but throws in that you should use the "bow-tie" diagram. All the diagram shows is that related acute angles of each quadrant, I don't see how that has any relation to this question.

 

[HallsofIvy]

Your answers are correct. And they are ratios! Every trig function is a ratio.

 

[Architeuthis Dux]

I would like to clarify what exactly is being asked in this question. Are we being asked to use the bow-tie diagram to determine the values of the trigonometric ratios for the given angles? If so, then the answers would be as follows:

a) sin 45 = 1 / \sqrt{2}
b) cos 60 = 1 / 2
c) tan 30 = 1 / \sqrt{3}
d) tan 45 = 1

The bow-tie diagram can help us understand the relationships between the angles and their corresponding trigonometric ratios. For example, in the first quadrant, we can see that sin 45 and cos 45 are both equal to 1 / \sqrt{2}. Similarly, in the second quadrant, we can see that cos 60 and sin 30 are both equal to 1 / 2.

However, it is important to note that the bow-tie diagram is just a visual aid and the values of the trigonometric ratios can also be determined using the unit circle or by using the trigonometric identities.

In conclusion, the values of the trigonometric ratios for the given angles are as stated above, but the use of the bow-tie diagram is not necessary to determine these values.