precalc practice midterm ii - weebly
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PreCalc Name_________________________________ Date__________________________Pd7
PRE-CALCULUSPRACTICETESTIINoCalculator
1. Fillinthetable.
x π ππ!!(π₯) πππ !!(π₯) π‘ππ!!(π₯)-1
π3
2π3
β22
1
β 3
2. Evaluatetheexpressionalgebraically.a.π‘ππ πππ !! β !
!b.πππ π‘ππ!! β !
!
3. Solvetheequationsalgebraically.
a. sec π = 2.Findallsolutions.
b. 2π ππ! π + 1 = 3overβ2π β€ π β€ 2π.
c. sin π = !!.Findallsolutions.
d. 2πππ !π + πππ π = 0over0 β€ π < 2π.
e. π ππ!π = 2πππ π + 2over0 β€ π < 2π.
f. sin (2π)β 1 = 0.Findallsolutions.
4. Ifcos πΌ = !!
π€βπππ 0 β€ πΌ β€ !!,πππ sin π½ = β !
! π€βπππ β !
!β€ π½ < 0;thenfind
a.sin πΌ + π½ π. cos πΌ + π½ π. sin πΌ β π½ π. cot (π½)
5. Provetheidentities.
a. sin (π₯) β csc (π₯)β πππ !(π₯) = π ππ!(π₯)
b. 1β πππ !π 1+ πππ‘!π = 1
c. sin πΌ + π½ + sin πΌ β π½ = 2 sinπΌ πππ π½
e.π‘ππ! π₯ πππ !(π₯)+ πππ‘!(π₯)π ππ!(π₯) = 1
6. Findtheexactvaluesofa.sin(75)b.cos !!!
!"
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