Chapter 10

Question 1

From a circle drawn with centre at the origin, what is sinθ?

Answer 1

The distance of point, P above the horizontal axis (y-coordinate).

Question 2

From a circle drawn with centre at the origin, what is cosθ?

Answer 2

The distance of point P to the right of the vertical axis (x-coordinate).

Question 3

What is the period and amplitude of sine?

Answer 3

360 and 1.

Question 4

What relationships are there involving sine?

Answer 4

.sinx ≡ sin(180 - x).
.sin x ≡ sin(x + 360).
.sin(180+x) ≡sin(-x) ≡ -sinx.

Question 5

What is the period and amplitude of cosine?

Answer 5

360 and 1.

Question 6

What relationships are there involving cosine?

Answer 6

.cos x ≡ cos(-x).
.cos x ≡ cos(x + 360).
.cos(180-x) ≡ cos(180+x) ≡ -cosx.

Question 7

What relationships relate sin x and cos x?

Answer 7

.sin x ≡ cos (90 - x).
.cos x ≡ sin (90 - x).

Question 8

What is the definition of tan x?

Answer 8

tan x ≡sin x/cos x.

Question 9

What is the period of tan and what are the asymptotes?

Answer 9

.180.
.x = 90,270 etc.

Question 10

What is tan x also equal to?

Answer 10

tan x = tan (x + 180) = tan (x + 360).

Question 11

What are the exact trig values for sin?

Answer 11

.0 - 0.
.30 - 1/2.
.45 - √2/2.
.60 - √3/2.
.90 - 1.
.120 - √3/2.
.135 - √2/2.
.150 - 1/2.
.180 - 0.

Question 12

What are the exact trig values for cos?

Answer 12

.0 - 1.
.30 - √3/2.
.45 - √2/2.
.60 - 1/2.
.90 - 0.
.120 - -1/2.
.135 - -√2/2.
.150 - -√3/2.
.180 - -1.

Question 13

What are the exact trig values for tan?

Answer 13

.0 - 0.
.30 - √3/3.
.45 - 1.
.60 - √3.
.90 - .
.120 - -V3.
.135 - -1.
.150 - -√3/3.
.180 - 0.

Question 14

What is the Pythagorean identity?

Answer 14

sin2x + cos2x = 1 for all x.