# 1 Pre-Calculus LAB 2 NAME ______________________________________ 1) Without a calculator find the exact value of: 1 1 1 1 sin (1) cos (1) tan (1) sec ( 2) − − − − + + + Answer ________________________

1 Pre-Calculus LAB 2 NAME ______________________________________ 1) Without a calculator find the exact value of: 1 1 1 1 sin (1) cos (1) tan (1) sec ( 2) − − − − + + + Answer ____________________________________ 2) Find the exact value, if any, of each composite function. If there is no value, say “undefined”. Give exact values. 1 5 cos (cos )) 4 −  Answer ____________________________________ 1 4 tan(sin ( )) 5 − − Answer ____________________________________ 3) Write the trigonometric expression as an algebraic expression in terms of u. 1 tan(csc ( )) u − 2 4. Solve each equation on the given interval sin(2 ) cos 2sin 1 0 x x x − − + = over 0 2  x  Answer __________________________ Q5. sec( ) 2 12 x  − = over Reals Answer __________________________ 6. Write an equation of a sinusoidal graph with the following properties: Amplitude: 4 Period: 6 Phase Shift: -2 Equation:_______________________________________________________ 7. Graph = 3 sin (2 ( − 4 )) + 1 over the inverval −2 ≤ ≤ 2π. Be sure to lable both axis. Specify amplitude, period, phase shift, and vertical shift (if applicable). 3 8. Write a possible sinusoidal equation for the following graph. Equation:_______________________________________________________ Q9. (Section 7.5) Find the exact value of each expression sin(165 ) 4 10.(Section 7.4) Establish each identity. You may only manipulate one side and show your individual steps. Do any two of the three identities. 2 2 2 5cos 3sin 3 2cos    + = + 1 cos sin 2csc sin 1 cos      − + = − csc sin cos cot     − =

1 Pre-Calculus LAB 2 NAME ______________________________________ 1) Without a calculator find the exact value of: 1 1 1 1 sin (1) cos (1) tan (1) sec ( 2) − − − − + + + Answer ________________________
1 Pre -Calculus LAB 2 NAME ______________________________________ 1) Without a calculator find the exact value of: Answer ____________________________________ 2) Find the exact val ue, if any, of each composite function. If there is no value, say “undefined”. Give exact values. Answer ____________________________________ Answer ___________ ________________ _________ 3) Write the trigonometric expression as an algebraic expr ession in terms of u. 1 1 1 1 sin (1) cos (1) tan (1) sec ( 2 ) − − − − + + + 1 5 cos (cos )) 4  − 1 4 tan(sin ( )) 5 − − 1 tan(csc ( )) u − 2 4. Solve each equation on the given interval over Answer ___________ _______________ Q5. over Reals Answer ___________ _______________ 6. W rite an equation of a sinusoidal graph with the following properties: Amplitude: 4 Peri od: 6 Phase Shift: -2 Equation:_______________________________________________________ 7. G raph = 3sin (2(− 4))+ 1 over the inverval −2≤ ≤ 2π . Be sure to lable both axis. Specify amplitude, period, phase shift, and vertical shift (if applicable). sin(2 ) cos 2 sin 1 0 x x x − − + = 02 x   sec( ) 2 12 x  −= 3 8. Write a possible sinusoidal equation for the following graph. Equation:_______________________________________________________ Q9. (Section 7.5) Find the exact value of each expression sin(165 ) 4 10. (Section 7.4) Establish each identity. You may only manipulate one side and show your individual steps. Do any two of the three identities. 2 2 2 5 cos 3sin 3 2 cos   + = + 1 cos sin 2 csc sin 1 cos    − += − csc sin cos cot    −= 