Chapter 6 - Trigonometric Functions

Question 1

sec x =?

Answer 1

1/cos x

Question 2

cosec x = ?

Answer 2

1/sin x

Question 3

cot x = ?

Answer 3

1/tanx

also = cos x/sin x

Question 4

Describe the graph of sec x

Answer 4

• symmetry in y axis
• period = 360 or 2π radians
• vertical asymptotes at all points where cos x = 0 (90, 270 degrees etc)
• range of y = sec x is -1<=y<=1

Question 5

Describe the graph of cosec x

Answer 5

• period of 360 degrees
• vertical asymptotes for all values of x where sin x = 0
• range of y = cosec x is -1 <= y <= 1

Question 6

Describe graph of y = cot x

Answer 6

• Period 180 degrees
• Vertical asymptotes at values of x where tan x = 0
• Range of y = cot x is y € R

Question 7

When does sec x = k have no solution?

Answer 7

For values of k between -1 and 1

Question 8

When does cosec x = k have no solution?

Answer 8

For values of k between -1 and 1

Question 9

Formula linking sec²x and tan²x

Answer 9

sec²x = 1 + tan²x

Question 10

Formula linking cot²x and cosec²x

Answer 10

cosec²x = 1 + cot²x

Question 11

Describe the function arcsin x

Answer 11

• inverse function of sinx
• domain of -1<= x<= 1
• range of -90 to +90 degrees

Question 12

Describe the function arccos x

Answer 12

• inverse funcation of cos x
• domain -1<=x<=1
• range is 0 to 180 degrees

Question 13

Describe the function arctan x

Answer 13

• inverse function of tan x
• domain is x € R
• range is -90 to +90