Math 021
MATH - 1022
Test 2/100 points
Spring 2021
Due by Saturday, March 6th @ 11:59pm.
Directions: Please do your own work. Do not solicit help from anywhere or anyone or from any
other source or classmates to help you with the Test. You could use you textbook, notes and any
other online sites to help you familiarize with the topics, but do not directly use these questions
to seek assistance. You may use a scientific calculator. Please show all work completely. Once
done, please send it to me via email ( XXXXXXXXXX) in PDF form with “Test 2 Math
1022_your name” as the subject. Ensure that all problems are done in order and your Test is
legible.
Name: _________________________________
1) State the domain and range, and draw the graph of xy 1sin −= by clearly labeling all
important points XXXXXXXXXXpoints)
For #2 - #8, Find Exactly. You must justify your answers to receive credit XXXXXXXXXXpoints)
2) ( )1tan 1 −−
mailto: XXXXXXXXXX
3) 3arcsin
2
−
4) 1arccos 1
2
−
5)
−
4
5coscos 1 π
6)
−−
4
tansin 1 π
XXXXXXXXXX1sin tan 3− −
XXXXXXXXXX1sinsin 1 −−
For #9 - #12, solve each equation alge
aically for the general solutions.
XXXXXXXXXXsin1tan =++ xx XXXXXXXXXXpoints)
10) xx sin2sin2 2 = XXXXXXXXXXpoints)
11) 02sec3 =−x XXXXXXXXXXpoints)
12) 01sectan 2 =−+ xx XXXXXXXXXX8 points)
For #13 - #15, solve each equation alge
aically for the interval [ )0,2π .
13) cos3 cos 2 cos 0x x x+ + = XXXXXXXXXXpoints)
14) sin 2 cos 0α α− = XXXXXXXXXXpoints)
XXXXXXXXXXtan 2 3 6x − = XXXXXXXXXXpoints)
For Problems #16-#18, prove the identities
16) θθθθ 2sec)cot(tantan = XXXXXXXXXXpoints)
17) xxxx cscseccottan = XXXXXXXXXXpoints)
18) tt
tt
tt tancot
cossin
sincos 22
−=
− XXXXXXXXXXpoints)
19) a) Find ( )sin 195 exactly using a sum identity XXXXXXXXXXpoints)
b) Find ( )0cos 75 using a difference identity XXXXXXXXXXpoints)
20) Given
5sin
3
θ = and θ in quadrant 2, find sin 2 ,cos 2 tan 2andθ θ θ (8 points)