Trigonometric identities

Show that

where N is an integer to be found.

State the two values of x between 0° and 360° for which the value of N in part (b) is not valid.

The curve with equation

for 360 x 360 is shown below.

Point A on the curve has coordinates (a, 0.5)

Find the value of a

State the value of sin (180 a)

Find the exact value of sin (b 180)

Find the exact value of cos b

Given that

Express y in terms of sin .

Hence, prove that

Show that

Use the substitution

to show that

can be written as

where k is a constant to be found.

Hence, show

where c is a constant.

Given that

use the quotient rule to show that

2 10 (b) The region enclosed by the curve y tan x and the horizontal line, which intersects the curve at x and x is shaded in the diagram below.

Show that the area of the shaded region is

Fully justify your answer.

Show that the equation

can be written in the form

Hence, given x is obtuse and

find the exact value of tan x

Fully justify your answer.