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Talking about Trigonometry

Why is this course important? Let us look at the history of trig.
Trigonometric tables were created over two thousand years ago for computations in astronomy.	The kind of trigonometry needed to understand positions on a sphere is called spherical trigonometry.
The stars were thought to be fixed on a crystal sphere of great size, and that model was perfect for practical purposes.	Spherical trigonometry is rarely taught now since its job has been taken over by linear algebra
Only the planets (Mercury, Venus, Mars, Jupiter, Saturn, the Moon, and the Sun) moved on the sphere.	Nonetheless, one application of trigonometry is astronomy.

 

Table: Values at special angles

x	sin(x)	cos(x)	tan(x)	cot(x)	sec(x)	csc(x)
0	0	1	0		1
2/3	sqrt(3)/2	-1/2	-sqrt(3)/3	-2	2	sqrt(3)/3
3/4	sqrt(2)/2	-sqrt(2)/2	-1	-1	-sqrt(2)	sqrt(2)
5/6	1/2	-sqrt(3)/2	-sqrt(3)/3	-sqrt(3)	-2	-sqrt(3)/3
2	0	-1	0		1

Questions

Q1	a	b	c	d	e
Q2	a	b	c	d	e
Q3	a	b	c	d	e

Note: Questions in red are OPTIONAL	A	B	C	D	E
Question #1 How would this table be altered if the figure was flipped so that Q was on right of the top of the circle?	The length of the hypotenuse would change.	The altitude QR would change.	The center O of the circle would move.	The sign of the cosine would change.	All of the above.
Question #2 In the table the sin never has a negative sign. Why not?	Because sin(x) is always => 0.	Because cos(x) is used when values <0 are needed.	Because the square root can't be used for negative numbers.	Because the headers of the table should be in alphabetical order.	None of the above.
Question #3 X labels the included angle in the figure and the table. This angle is measured in:	Degrees	Radians	Minutes	Congruential factoids	Liters