Trigonometry

Question 1. $~-\pi/3~$

Question 2. $~7\pi/6~$

$\sqrt3/2$

$-\sqrt3~/2$

$-\sqrt6$

$1\sqrt2$

Question 3. $~7\pi/4~$

${-1\over\sqrt2}$

${-\sqrt3\over~2}$

${\sqrt3\over~2}$

${1\over\sqrt2}$

Question 4. $~9\pi~$

Question 5. Find all values of x in the range $0\le~x\le~\pi/2$ for which $\sin~~(4x-\pi/3)=1/2~$

$~0~$

$\pi/8$

$\pi/6$

$5\pi/24~$

$\pi/3~$

$7\pi/24$

$3\pi/8~$

$\pi/2~$

$5\pi/6$

Question 6. Find all values of x in the range $0\le~x\le~2\pi$ for which $2{\cos}^2~x=\cos~x~+1~$

$0$

$2\pi/3$

$~3\pi/4~$

$4\pi/3$

$~\pi/2$

$~5\pi/4$

$~3\pi/2$

$~5\pi/3$

$2\pi$

Question 7. Find all values of x in the range $0\le~x\le~2\pi$ for which $\cos^4~x-\sin^4~x=1$

$0$

$~\pi/3$

$~\pi/2~$

$~2\pi/3~$

$~3\pi/4~$

$\pi$

$~4\pi/3~$

$~3\pi/2$

$2\pi$

$~\sqrt2$

$~2$

$~1/2$

$2\sqrt2$

$~\sqrt2~/2$

$~{2\over~\sqrt2}$

$~0$

$~\pi/6$

$\pi/4$

$~\pi/3$

$~\pi/2$

Question 9. Using question 8, or otherwise, find the maximum
value of $2\sin~x+2\cos~x$

$~\sqrt2$

$~2$

$~1/2$

$2\sqrt2$

$~\sqrt2~/2$

$~{2\over~\sqrt2}$

Question 10. If $~\cos~A=1/2~$ find the exact value of $\cos~(3A)$ .

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Mathematics Institute

Trigonometry

Score 8 or more out of 11 to pass.

Section A: State cos of the following numbers.

Section B: Work out the values before looking at choices, plugging in each choice and seeing if it works tests nothing!

Section C:

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