Graphing Trig Functions

(2 sin x +1)(cos x − 1)

0, 7π/6, 11π/6, 2π Hint: The form of the equation is (A sin x + B)(B cos x - B)

(tan x)(√2 sin x − 1)

0, π/4, 3π/4, π, 2π Hint: The form of the equation is (A tan x)(B sin x - A)

(2sin x +√3) / (cos x +1)

4π/3, 5π/3 Hint: The form of the equation is (A sin x + B) / (C cos x + C)

(2sin x +√3) / (cos x − 1)

4π/3, 5π/3 Hint: The form of the equation is (A sin x + B) / (C cos x - C)

c

Type the letter (without any punctuation) of the TRUE statement. a) There are two functions of sin x and two functions of sin 2x. b) The amplitude of the purple function is a whole number. c) The green function is of the form f(x) = A sin (2x) + C. d) All of the functions represent f (x) = A sin (bx ) + C. e) The absolute value of C, the vertical shift, is 2 for all functions, assuming the form f (x) = A sin (bx ) + C. HINT: the answers are found in the flashcard set.

sin 3x + sin x - cos x

π/12, 5π/12, π/2, 13π/12, 17π/12, 3π/2 Hint: The form of the equation is sin Ax + sin Bx - cos Bx

(2 sin x − √3)(√2 cos x + 1)

π/3, 2π/3, 3π/4, 5π/4 Hint: The form of the equation is (A sin x + B)(√A cos x + C)

cos 3x + cos x

π/4, π/2, 3π/4, 5π/4, 3π/2, 7π/4 Hint: The form of the equation is cos Ax + cos Bx

(sec x)² + 3(csc x)² - 8

π/4, π/3, 2π/3, 3π/4, 5π/4, 4π/3, 5π/3, 7π/4 Hint: The form of the equation is A(sec x)² + B(csc x)² + C

cos 3x + cos x - cos 2x

π/4, π/3, 3π/4, 5π/4, 5π/3, 7π/4 Hint: The form of the equation is cos Ax + cos Bx + cos Cx

(cot x)(2 sin x − 1)

π/6, π/2, 5π/6, 3π/2 Hint: The form of the equation is (A cot x)(B sin x - A)

(sin x + cos x) / (sin x)

Hint: Another way of writing 1 + cot x

(sin x - cos x) / (sin x)

Hint: Another way of writing 1- cot x

(cos x)²

Hint: The equation does not contain a constant.

(sin x)²

Hint: The equation does not contain a constant.

(2 cos x − √3)(csc x + 1)

Hint: The form of the equation is (A cos x + B)(C csc x + C)

4(sin x)² − 3

Hint: The form of the equation is A (sin x)² + B

(tan x)² − 1

Hint: The form of the equation is A (tan x)² + B

2(cos x)² − 1

Hint: The form of the equation is A(cos x)² + B

3(cos x)² - 2

Hint: The form of the equation is A(cos x)² + B

4(cos x)² − 1

Hint: The form of the equation is A(cos x)² + B

2(sin x)² + (cos x)²

Hint: The form of the equation is A(sin x)² + B(cos x)²

2(sin x)² − (cos x)²

Hint: The form of the equation is Z(sin x)² + Y(cos x)²

2(sin x) +√3

The black function is (sin x)² + 2(sin x) + 1. The pink function is not a square of sin x. Instead, it is of the form A(sin x) + B. Write the equation for the pink function.

3 − sin x

The pink curve on the bottom represents sin x. The blue curve represents 1 − sin x. What does the purple curve represent?