Practice Test #3

1. Find the exact value of each expression. Express all angles in radians.

a. cos 31π

6( ) b. sin −π( ) c.

sec − π

4( ) d.

tan 5

3π( ) e.

arccos 0( ) f.

arccsc 2

3( ) g.

sec arctan 8( )( ) h.

arccos cos − π

3( )( )

2. Sketch at least one period of each function. State the period and the range.

a. y = 1

3cosx( ) + 1 b.

y = tan 2x −π( )

3. Find sin θ given that tan θ = 3

7 and θ is not a first quadrant angle.

4. Find an equivalent trigonometric expression. (Multiple Choice)

a. sinx + cosx cotx

I. cotx II. cscx III. 2sinx IV. cos2 x + 1

b. 2sin2 α− sinα− 3

I. sinα− 3( ) 2sinα+ 1( ) II.

2 sinα+ 1( ) sinα− 3( )

III. 2sinα− 3( ) sinα+ 1( ) IV.

sinα 2sinα−1( )− 2

c.

sec θ

tan θ+ cot θ I. 1 II. sin θ III. sec θ IV. 2sec θ