Q: Find the exact value: $$\\cot 60^\\circ - \\cos 45^\\circ.$$

$$\\frac{2}{3} - \\frac{\\sqrt{2}}{2}$$

Question 1

Convert $$36^\circ to $$radians. Express your answer as a multiple of $$\pi.$$

Accepted Answer

$$\frac{\pi}{5}$$

Question 2

A car wheel has a radius of 15 inches. Through what angle (in degrees, to the nearest tenth) does the wheel turn when the car rolls forward 4 feet?

Accepted Answer

$$183.3^\circ$$

Question 3

Find the area of a sector of a circle of radius 17 inches formed by a central angle of $$120^\circ. $$Round your answer to two decimal places.

Accepted Answer

$$302.64$$ square inches

Question 4

Given $$\tan \theta \u003e 0$$ and $$\sin \theta \u003c 0$$, in which quadrant does $$\theta$$ lie?

Accepted Answer

Quadrant III

Question 5

Find the exact value: $$\sin(-\frac{\pi}{2}).$$

Accepted Answer

$$-1$$

Question 6

Evaluate $$\cos(2\pi/7) to $$two decimal places.

Accepted Answer

$$0.37$$

Question 7

Given $$\cos t = \frac{4}{5}$$ and $$\sin t \u003c 0$$, find $$\sin t.$$

Accepted Answer

$$-\frac{3}{5}$$

Question 8

Find the amplitude of $$y = -3 \cos x + \frac{\pi}{4}.$$

Accepted Answer

$$3$$

Question 9

Find the period of $$y = -5 \sin(6x + \frac{\pi}{2}).$$

Accepted Answer

$$\frac{\pi}{3}$$

Question 10

Find the exact value: $$\cot 60^\circ - \cos 45^\circ.$$

Accepted Answer

$$\frac{2}{3} - \frac{\sqrt{2}}{2}$$

Question 11

If $$\sin \theta = -\frac{12}{13}$$ and $$\theta is in $$quadrant III, what is $$\cos \theta$$?

Accepted Answer

$$-\frac{5}{13}$$

Question 12

Find the length of the arc on a circle of radius $$12$$ meters intercepted by a central angle of $$75^\circ. $$Round your answer to three decimal places.

Accepted Answer

$$15.708 m$$

Question 13

Evaluate $$\sin t$$ for $$t = \frac{11\pi}{6}.$$

Accepted Answer

$$-\frac{1}{2}$$

Question 14

Which of the following is the correct value for $$y = \tan$$^{-1}$$(-1)$$?

Accepted Answer

$$-\frac{\pi}{4}$$

Question 15

Given $$\tan t = -5$$ and $$\cos t \u003e 0$$, find $$\sec t.$$

Accepted Answer

$$\sqrt{26}$$

Question 16

Find the exact value: $$\sin(330^\circ).$$

Accepted Answer

$$-\frac{1}{2}$$

Question 17

If $$\csc \theta = \frac{8}{15}$$ and $$\theta is in $$quadrant II, what is $$\sin \theta$$?

Accepted Answer

Question 18

Which of the following graphs best represents $$y = 2 \tan(4x)$$?

Accepted Answer

Image 15

Question 19

Find the amplitude of $$y = -5 \sin 3(x + \pi).$$

Accepted Answer

$$5$$

Algebra and Trigonometry Exam 1 Review – Step-by-Step Guidance

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