Pre-Calculus Lesson 6 .io



Chapter 5 Test – Solutions Form #1

1) cos(x) + sin(x)tan(x) = sec(x)

cos(x) + sin(x)[pic] =

[pic]+ [pic] =

[pic]=

[pic]=

sec(x) [4 points]

2) csc(2x) – cot(2x) = tan(x)

[pic]=

[pic]=

[pic]=

[pic]=

[pic]=

tan(x) [5 points]

(3) [pic] =

[pic] =

[pic] =

[pic] [4 points]

(4) [pic]

[pic]=

[pic]=

[pic] [3 points]

(5) sin [pic]= sin[pic]

sin[pic]cos[pic]– cos[pic]sin[pic] =

[pic][pic]–[pic][pic] =

[pic] [4 points]

(6) cos[pic]= cos[pic]=

cos[pic]cos[pic]– sin[pic]sin[pic] =

[pic][pic] – [pic][pic] =

[pic] [4 points]

7) 2sin(5x) cos(3x) =

sin(8x) + sin(2x) [4 points]

(8) cos(7x) + cos(3x) =

2cos[pic]cos[pic]=

2cos(5x) cos(2x) [4 points]

(9) Given: cos x = [pic] and [pic]

cos[pic] = [pic]

= [pic]

= [pic]

= [pic] or [pic] [4 points]

(10) Given: sin x = [pic] and [pic]

sin[pic] = [pic]

= [pic]

= [pic]

= [pic]

= [pic] [4 points]

(11) 2sinx cos x + cos x = 0

cos x(2 sin x + 1) = 0

cos x = 0 or 2 sin x + 1 = 0

x = [pic] or sin x = –[pic]

x = [pic] x = [pic]

where k is any integer [6 points]

(12) Solve on [0, 2π): sin(x)tan[pic]= [pic]

[pic]= [pic]

1 – cos x = [pic]

cos x = [pic]

x = [pic] [4 points]

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