PreCalc Name_________________________________ Date__________________________Pd7

PRE-CALCULUSPRACTICETESTIINoCalculator

1. Fillinthetable.

x 𝑠𝑖𝑛!!(𝑥) 𝑐𝑜𝑠!!(𝑥) 𝑡𝑎𝑛!!(𝑥)-1

𝜋3

2𝜋3

−22

1

− 3

2. Evaluatetheexpressionalgebraically.a.𝑡𝑎𝑛 𝑐𝑜𝑠!! − !

!b.𝑐𝑜𝑠 𝑡𝑎𝑛!! − !

!

3. Solvetheequationsalgebraically.

a. sec 𝜃 = 2.Findallsolutions.

b. 2𝑠𝑖𝑛! 𝜃 + 1 = 3over−2𝜋 ≤ 𝜃 ≤ 2𝜋.

c. sin 𝜃 = !!.Findallsolutions.

d. 2𝑐𝑜𝑠!𝜃 + 𝑐𝑜𝑠𝜃 = 0over0 ≤ 𝜃 < 2𝜋.

e. 𝑠𝑖𝑛!𝜃 = 2𝑐𝑜𝑠𝜃 + 2over0 ≤ 𝜃 < 2𝜋.

f. sin (2𝜃)− 1 = 0.Findallsolutions.

4. Ifcos 𝛼 = !!

𝑤ℎ𝑒𝑟𝑒 0 ≤ 𝛼 ≤ !!,𝑎𝑛𝑑 sin 𝛽 = − !

! 𝑤ℎ𝑒𝑟𝑒 − !

!≤ 𝛽 < 0;thenfind

a.sin 𝛼 + 𝛽 𝑏. cos 𝛼 + 𝛽 𝑐. sin 𝛼 − 𝛽 𝑑. cot (𝛽)

5. Provetheidentities.

a. sin (𝑥) ∙ csc (𝑥)− 𝑐𝑜𝑠!(𝑥) = 𝑠𝑖𝑛!(𝑥)

b. 1− 𝑐𝑜𝑠!𝜃 1+ 𝑐𝑜𝑡!𝜃 = 1

c. sin 𝛼 + 𝛽 + sin 𝛼 − 𝛽 = 2 sin𝛼 𝑐𝑜𝑠𝛽

e.𝑡𝑎𝑛! 𝑥 𝑐𝑜𝑠!(𝑥)+ 𝑐𝑜𝑡!(𝑥)𝑠𝑖𝑛!(𝑥) = 1

6. Findtheexactvaluesofa.sin(75)b.cos !!!

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