Chapter 7 Practice Quiz
Simplify the following two expressions.
= -sin(x) sin(x) = -sin2(x)
1. sin(-x) cos(
2. tan4x + 2tan2x + 1 = (tan2x + 1)(tan2x +1) = (sec2x)(sec2x) = sec4x
Verify the following trig expressions.
3. Cos(x) – cos(x) sin2(x) = cos3x
= cos(x) (1-sin2x)
= cos(x) (cos2x)
= cos3x = cos3x
4. Sec(
– [tan(
sin(
] = sin(x)
= csc(x) – (cot(x) cos(x))
= csc(x) – ((cos(x)/sin(x)) x (cos(x))
= csc(x) – (cos2x/sinx)
= 1/sin(x) – (cos2x/sinx)
=(1 - cos2x)/sinx
= sin2x/sinx
= sin(x) = sin(x)
Find the exact values for the following trig measures.
5. Sin(2100 + 450)
= sin(210)cos(45) + sin(45)cos(210)
= -√3/2 x √2/2 + √2/2 x -1/2
= -√6/4 + -√2/4
= (-√6-√2)/4
6. Cos(1650)
= cos(120 + 45)
= cos(120)cos(45) – sin(120)sin(45)
= -√3/2 x √2/2 – ½ x √2/2
= -√6/4 - √2/4
= (-√6-√2)/4