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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 (
[email protected]) 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. (6 points) For #2 - #8, Find Exactly. You must justify your answers to receive credit. (21 points) 2) ( )1tan 1 −− mailto:
[email protected] 3) 3arcsin 2 − 4) 1arccos 1 2 − 5) − 4 5coscos 1 π 6) −− 4 tansin 1 π 7) ( )( )1sin tan 3− − 8) ( )( )1.1sinsin 1 −− For #9 - #12, solve each equation algebraically for the general solutions. 9) ( ) 0)1(sin1tan =++ xx (6 points) 10) xx sin2sin2 2 = (6 points) 11) 02sec3 =−x (6 points) 12) 01sectan 2 =−+ xx (8 points) For #13 - #15, solve each equation algebraically for the interval [ )0,2π . 13) cos3 cos 2 cos 0x x x+ + = (7 points) 14) sin 2 cos 0α α− = (6 points) 15) ( )2 tan 2 3 6x − = (5 points) For Problems #16-#18, prove the identities 16) θθθθ 2sec)cot(tantan =+ (5 points) 17) xxxx cscseccottan =+ (5 points) 18) tt tt tt tancot cossin sincos 22 −= − (5 points) 19) a) Find ( )sin 195 exactly using a sum identity. (3 points) b) Find ( )0cos 75 using a difference identity. (3 points) 20) Given 5sin 3 θ = and θ in quadrant 2, find sin 2 ,cos 2 tan 2andθ θ θ (8 points)