Chapter 11 Multiple choice questions

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. Select the correct expression for cosine θ from the list below:

$\frac{\text{opposite}}{\text{hypotenuse}}$ correct incorrect

$\frac{\text{adjacent}}{\text{hypotenuse}}$ correct incorrect

$\frac{\text{opposite}}{\text{adjacent}}$ correct incorrect

$\frac{\tan \theta }{\sin \theta }$ correct incorrect

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. Calculate the value of θ in degrees given that:
${\cos }^2\theta +\frac{9}{4}=3$

60° correct incorrect

49.6° correct incorrect

0.52° correct incorrect

30° correct incorrect

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. Re-express the angle 270° in radians.

$\frac{3}{2}\pi$ correct incorrect

$\frac{5}{4}\pi$ correct incorrect

$\frac{2}{3}\pi$ correct incorrect

$\frac{3}{4}\pi$ correct incorrect

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. A right-angled triangle has two shorter sides of length 4 m and 8 m. How long is the hypotenuse?

80 m correct incorrect

8.94 m correct incorrect

6.93 m correct incorrect

12 m correct incorrect

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. A 20 m long rope is strung between a point on the ground and the top of a building. The attachment on the ground is 10 m from the base of the building, which rises up from the ground at 90°.
How tall is the building?

3.2 m correct incorrect

19.7 m correct incorrect

17.3 m correct incorrect

30 m correct incorrect

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. Determine the Cartesian coordinates of the following point, which is given in spherical polar coordinates: (4, 60°, 135°).

$\left(-\sqrt{6},\sqrt{6},2\right)$ correct incorrect

$\left(-\sqrt{\frac{3}{2}},\sqrt{\frac{3}{2}},2\right)$ correct incorrect

$\left(-\sqrt{2},\sqrt{2},2\sqrt{3}\right)$ correct incorrect

$\left(-\sqrt{6},\sqrt{6},2\sqrt{3}\right)$ correct incorrect

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. Determine the spherical polar coordinates (in 3D) of the following point, which is given in Cartesian coordinates: (5, $\sqrt{3}$, 6).

(64, 41.4°, 19.8°) correct incorrect

(5.3, 43.0°, 19.8°) correct incorrect

(8, 19.8°, 43.0°) correct incorrect

(8, 41.4°, 19.1°) correct incorrect

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. Select the correct statement of the cosine rule.

c² = a² + b² + 2ab cos C correct incorrect

c² = a² + b² - 2ab cos C correct incorrect

c² = a² + b² - ab cos C correct incorrect

c² = a² + b² - 2ac cos C correct incorrect

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. Calculate the value of θ in degrees.

117° correct incorrect

63° correct incorrect

153° correct incorrect

27° correct incorrect

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. Using trigonometric identities, select the incorrect statement from the list below. (Do not use your calculator.)

cos 80 = cos² 40 - sin² 40 correct incorrect

sin 80 = 2 sin 40 cos 40 correct incorrect

cos 80 = 1 - sin² 40 correct incorrect

cos 80 = cos 30 cos 50 - sin 30 sin 50 correct incorrect