Test: Trigonometry - Ambitious

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Question 1:   Convert the angle $176°15\text{'}56\text{'}\text{'}$ to the decimal degree format
$176.1556$
$176.2$
$176.1$
$176.266$
Question 2:   Convert the angle $18.315$ to the degrees, minutes and seconds
$18°18\text{'}54\text{'}\text{'}$
$18°3\text{'}15\text{'}\text{'}$
$18°19\text{'}03\text{'}\text{'}$
$18°20\text{'}15\text{'}\text{'}$
Question 3:   Convert $176°15\text{'}56\text{'}\text{'}$ to the radians to $2$ d.p.
$0.22\pi$
$0.2\pi$
$0.19\pi$
$0.21\pi$
Question 4:   Convert $3.42$ radians to the degrees to $2$ d.p.
$200°$
$195°$
$195.95°$
$196.05°$
Question 5:   Find the value of $\mathrm{cot}\left(\frac{\pi }{3}\right)$
$1.1124$
$0.6732$
$1.276$
$0.5773$
Question 6:   Find the value of $\mathrm{cos}42°$ to $4$ d.p.
$0.7413$
$0.7429$
$0.7431$
$0.743$
Question 7:   Hypotenuse of the right angled triangle is $16.3$ and one side of the triangle is $7.4$. Find the length of the other side
$14.52$
$12.8$
$13.49$
$23.7$
Question 8:   Simplify the following identity: ${\mathrm{tan}}^{2}\theta -{\mathrm{sin}}^{2}\theta =\frac{{\mathrm{sin}}^{2}\theta }{{\mathrm{cos}}^{2}\theta }-{\mathrm{sin}}^{2}\theta$
${\mathrm{sin}}^{4}\theta {\mathrm{sec}}^{2}\theta$
${\mathrm{cos}}^{2}\theta {\mathrm{csc}}^{2}\theta$
$\mathrm{tan}\theta$
${\mathrm{sin}}^{4}\theta$
Question 9:   Simplify the following identity: ${\left(\mathrm{sin}\theta -\mathrm{cos}\theta \right)}^{2}+{\left(\mathrm{sin}\theta +\mathrm{cos}\theta \right)}^{2}$
$\mathrm{sin}\theta -\mathrm{cos}\theta$
$\mathrm{sin}\theta$
$0$
$2$
Question 10:   Simplify the following identity: $1-\frac{\mathrm{sin}\theta \mathrm{tan}\theta }{1+\mathrm{sec}\theta }$
$\mathrm{sec}\theta$
$\mathrm{cos}\theta$
$\mathrm{tan}\theta$
$\mathrm{sin}\theta$