1. find cot θ if csc θ = square root of five divided by two and tan θ > 0. (6 points)

a) square root of five
b) 2
c) square root of five divided by five
d) one half

2. find cos θ if sin θ = negative twelve divided by thirteen and tan θ > 0. (6 points)

a) negative five divided by twelve
b) negative five divided by thirteen
c) twelve divided by five
d) negative thirteen divided by twelve

3. use basic identities to simplify the expression. (6 points)
tangent of theta divided by secant of theta.

a) cos3θ
b) tan2θ
c) sec2θ
d) sin θ

4. simplify the expression. (6 points)
sine of x to the second power minus one divided by cosine of negative x

a) -sin x
b) cos x
c) sin x
d) -cos x

5. find all solutions in the interval [0, 2π). (6 points)
sin2x + sin x = 0

a) x = 0, π, four pi divided by three , five pi divided by three
b) x = 0, π, pi divided by three , two pi divided by three
c) x = 0, π, pi divided by three , five pi divided by three
d) x = 0, π, three pi divided by two

6. find all solutions to the equation.
cos x = sin x (6 points)

a) pi divided by four plus n pi such that n equals zero, plus or minus one, plus or minus two to infinity
b) pi divided by four plus two n pi comma seven pi divided by four plus two n pi such that n equals zero, plus or minus one, plus or minus two to infinity
c) pi divided by two plus n pi such that n equals zero, plus or minus one, plus or minus two to infinity
d) three pi divided by four plus two n pi comma five pi divided by four plus two n pi such that n equals zero, plus or minus one, plus or minus two to infinity

7. find an exact value.
sin 105° (6 points)

a) quantity square root of six plus square root of two divided by four
b) quantity negative square root of six plus square root of two divided by four
c) quantity square root of six minus square root of two divided by four
d) quantity negative square root of six minus square root of two divided by four

8. find an exact value. (6 points)
tangent of seven pi divided by twelve

a) quantity two minus square root of three divided by four
b) -2 - square root of three
c) quantity two plus square root of three divided by four
d) 2 + square root of three

9. write the expression as the sine, cosine, or tangent of an angle. (6 points)
sin 57° cos 13° - cos 57° sin 13°

a) cos 70°
b) cos 44°
c) sin 44°
d) sin 70°

10. write the expression as the sine, cosine, or tangent of an angle. (6 points)
cos 94° cos 37° + sin 94° sin 37°

a) sin 131°
b) sin 57°
c) cos 131°
d) cos 57°

11. write the expression as the sine, cosine, or tangent of an angle. (6 points)
sin 5x cos x - cos 5x sin x

a) cos 6x
b) cos 4x
c) sin 6x
d) sin 4x

12. rewrite with only sin x and cos x. (6 points)
sin 2x - cos 2x

a) 2 sin2x - 2 sin x cos x + 1
b) 2 sin x
c) 2 sin2x + 2 sin x cos x - 1
d) 2 sin2x - 2 sin x cos x - 1

13. find the exact value by using a half-angle identity. (6 points)
cosine of pi divided by twelve

a) one half times the square root of quantity one plus square root of three
b) one half times the square root of quantity one minus square root of three
c) one half times the square root of quantity two plus square root of three
d) one half times the square root of quantity two minus square root of three

14. verify the identity. (7 points)
4 csc 2x = 2 csc2x tan x

15. verify the identity. (8 points)
cotangent of x divided by quantity one plus cosecant of x equals quantity cosecant of x minus one divided by cotangent of x

16. verify the identity. (7 points)
sin quantity x plus pi divided by two = cos x

i would really appreciate priority for this! you!