Name
Date
Trig Expressions Practice Quiz
For 1-2, simplify the trig expressions.
1. sin(x)cot(x)
sin(x) * (cos(x)/sin(x)) = sin(x)
2.
sec
𝑥−cos
𝑥
sec 𝑥
= (sec(x)/sec(x)) - cos(x)/sec(x) = 1 - cos^2(x) = sin^2(x)
3. Show the following identities are equivalent.
Sin3(x) + sin(x)cos2(x) = sin (x)
= sin(x) (sin^2(x) + cos^2(x))
= sin(x) (1)
= sin(x) = sin(x)
4. Find cos(-750)
= cos (-30 + -45) = cos(-30)cos(-45) - sin(-30)sin(-45)
= (rad(3)/2)(rad(2)/2) - (-1/2)(-rad(2)/2)
= rad(3)/4 - rad(2)/4
= (rad(6) - rad(2))/4
5. If cos(a) = 12/13 in quadrant 1, and sin(b) = -7/25 in quadrant 4, find sin(a – b).
Drawing triangles; cos(b) = 24/25; sin(a) = 5/13;
sin(a - b) = sin(a)cos(b) - sin(b)cos(a)
= (5/13)(24/25) - (-7/25)(12/13)
= 120/325 + 84/325
= 204/325