1 Marks Question

Question 11 Mark

Find the degree measure corresponding to the following radian measures: $(\text{Use}\ \pi=\frac{22}{7})$
$\frac{-5\pi}{6}$

Answer

We have,
$\pi$ reduans = 180º
$1^{\text{c}}=\big(\frac{180}{\pi}\big)^{\circ}$
Now,
$\Big(\frac{-5\pi}{6}\Big)^{\text{c}}=\Big(\frac{-5\pi}{6}\times\frac{180}{\pi}\Big)^{\circ}$
$=-150^{\circ}$

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Question 21 Mark

Find the radian measure corresponding to the following degree measures:
7°30'

Answer

We have,
$180^{\circ}=\pi^{\text{c}}$
$\therefore 1^{\circ}=\Big(\frac{\pi}{180}\Big)^{\text{c}}$
Now,
$7^{\circ}30^{'}=\Big(7\times\frac{\pi}{180}\Big)^{\text{c}}\times\Big(\frac{30}{60}\Big)^{\circ}$
$=\Big(7\frac{1}{2}\Big)^{\circ}\times\Big(\frac{\pi}{180}\Big)^{\text{c}}$
$=\Big(\frac{15}{2}\times\frac{\pi}{180}\Big)^{\text{c}}$
$=\frac{\pi}{24}$

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Question 31 Mark

Find the radian measure corresponding to the following degree measures:
300°

Answer

We have,
$180^{\circ}=\pi^{\circ}$
$\therefore 1^{\circ}=\Big(\frac{\pi}{180}\Big)^{\text{c}}$
Now,
$300^{\circ}=300\times\frac{\pi}{180}$
$=\frac{5\pi}{3}$

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Question 41 Mark

Find the radian measure corresponding to the following degree measures:
125°30'

Answer

We have,
$180^{\circ}=\pi^{\text{c}}$
$\therefore 1^{\circ}=\Big(\frac{\pi}{180}\Big)^{\text{c}}$
Now,
$125^{\circ}30^{'}=125^{\circ}\Big(\frac{30}{60}\Big)^{\circ}$
$=\Big(125\frac{1}{2}\Big)^{\circ}$
$=\Big(\frac{251}{2}\times\frac{\pi}{180}\Big)^{\text{c}}$
$=\frac{251\pi}{360}$

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Question 51 Mark

Find the degree measure corresponding to the following radian measures: $(\text{Use}\ \pi=\frac{22}{7})$
$\big(\frac{18\pi}{5}\big)$

Answer

We have,
$\pi$ reduans = 180º
$1^{\text{c}}=\big(\frac{180}{\pi}\big)^{\circ}$
Now,
$\Big(\frac{18\pi}{5}\Big)^{\text{c}}=\Big(\frac{18\pi}{5}\times\frac{180}{\pi}\Big)^{\circ}$
$=648^{\circ}$

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Question 61 Mark

Find the radian measure corresponding to the following degree measures:
35°

Answer

We have,
$180^{\circ}=\pi^{\circ}$
$\therefore 1^{\circ}=\Big(\frac{\pi}{180}\Big)^{\text{c}}$
Now,
$35^{\circ}=35\times\frac{\pi}{180}$
$=\frac{7\pi}{36}$

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Question 71 Mark

Find the radian measure corresponding to the following degree measures:
-56°

Answer

We have,
$180^{\circ}=\pi^{\text{c}}$
$\therefore 1^{\circ}=\Big(\frac{\pi}{180}\Big)^{\text{c}}$
Now,
$-56^{\circ}=-56\times\frac{\pi}{180}$
$=\frac{-14\pi}{45}$

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Question 81 Mark

Find the degree measure corresponding to the following radian measures: $(\text{Use}\ \pi=\frac{22}{7})$
$(-3)^c$

Answer

We have,
$\pi$ reduans $= 180^\circ$
$1^{\text{c}}=\big(\frac{180}{\pi}\big)^{\circ}$
Now,
$(-3)^{\text{c}}=\Big(-3\times\frac{180}{\pi}\Big)^{\circ}$
$=\Big(\frac{180}{22}\times7\times-3\Big)^{\circ}$
$=\Big(-171\frac{9}{11}\Big)^{\circ}$
$=-171^{\circ}\Big(\frac{9}{11}\times60\Big)^{'}$
$=-171^{\circ}49^{'}5^{"}$

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Question 91 Mark

Find the degree measure corresponding to the following radian measures: $(\text{Use}\ \pi=\frac{22}{7})$
$\frac{9\pi}{5}$

Answer

We have,
$\pi$ reduans = 180º
$1^{\text{c}}=\big(\frac{180}{\pi}\big)^{\circ}$
Now,
$\Big(\frac{9\pi}{5}\times\frac{180}{\pi}\Big)^{\circ}$
$=324^{\circ}$

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Question 101 Mark

Find the radian measure corresponding to the following degree measures:
135°

Answer

We have,
$180^{\circ}=\pi^{\text{c}}$
$\therefore 1^{\circ}=\Big(\frac{\pi}{180}\Big)^{\text{c}}$
Now,
$135^{\circ}=135\times\frac{\pi}{180}$
$=\frac{3\pi}{4}$

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Question 111 Mark

Find the degree measure corresponding to the following radian measures: $(\text{Use}\ \pi=\frac{22}{7})$
$1^\text{c}$

Answer

We have,
$\pi$ reduans = 180º
$1^{\text{c}}=\big(\frac{180}{\pi}\big)^{\circ}$
Now,
$(1)^{\text{c}}=\Big(1\times\frac{180}{\pi}\Big)^{\circ}$
$=1\times\frac{180\times7}{22}$
$=57^{\circ}\Big(\frac{3}{11}\times60\Big)$
$=57^{\circ}16^{'}\Big(\frac{4}{11}\times60\Big)^{"}$
$=57^{\circ}16^{'}21^{"}$

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Question 121 Mark

Find the degree measure corresponding to the following radian measures: $(\text{Use}\ \pi=\frac{22}{7})$
$11^c$

Answer

We have,
$\pi$ reduans $= 180^\circ$
$1^{\text{c}}=\big(\frac{180}{\pi}\big)^{\circ}$
Now,
$(11)^{\text{c}}=\Big(11\times\frac{180}{\pi}\Big)^{\circ}$
$=\Big(11\times180\times\frac{7}{22}\Big)^{\circ}$
$=630^{\circ}$

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Question 131 Mark

Find the radian measure corresponding to the following degree measures:
-300°

Answer

We have,
$180^{\circ}=\pi^{\text{c}}$
$\therefore 1^{\circ}=\Big(\frac{\pi}{180}\Big)^{\text{c}}$
Now,
$-300^{\circ}=-300\times\frac{\pi}{180}$
$=\frac{-5\pi}{3}$

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