PRACTICE EXAM 3
Math 1060-2, Fall 2007
This exam covers Chapter 5 of the text...
1. Use the given values, along with the fundamental identities to evaluate the remaining trigonometric functions.
sec(x) = −3and sin(x) = √10
10
(a) cos(x)
(b) csc(x)
(c) tan(x)
(d) cot(x)
2. Use the fundamental identities to simplify the expressions.
(a) cot(β)2
csc(β)2
(b) sin(x)sec(x) + cos(x)csc(x)
(c) cos(θ)2+cos(θ)2tan(θ)2
(d) 1 −2cos(u)2+cos(u)4
3. Verify the identities.
(a) cos(v)2−sin(v)2= 2cos(v)2−1
(b) cot(α)3
csc(α)=cos(α)(csc(α)2−1)
(c) sec(x)−cos(x) = sin(x)tan(x)
(d) cos(θ)−cos(θ)
1−tan(θ)=sin(θ)cos(θ)
sin(θ)−cos(θ)
(e) sec(t)2−cot(π
2−t)2= 1
4. Verify that the x-values are solutions to the equation: 2cos(4x)2= 1
(a) x=π
16
(b) x=3π
16
5. Find all solutions of the equation in the interval [0,2π).
(a) 2sin(x) + 1 = 0
(b) 3cot(x)2−1 = 0
(c) 2sin(x)2= 2 + cos(x)
(d) 2sin(x)2+ 3sin(x) + 1 = 0
