Trigonometry (Radians and Angles)

Fill in the Blank

Suppose you know that for a particular angle, $$\cos\theta=\frac{4}{5}$$ . The related triangle is shown.

If this triangle were superimposed on a circle so that the vertex of $$\theta$$ was the center of the circle, what would be the radius of the circle?

Multiple Choice

Set up the problem...

• sin X = 41/28
• tan X = 41/28
• cos X = 28/41
• sin X = 28/41

Multiple Choice

What type of angle is this?

• Straight

• Acute

• Right

• Left

Multiple Choice

The input of the trigonometric functions represents a(n) ...

• Angle measure

• Real number

• Length

• Area

Multiple Choice

The output of the trigonometric functions are ...

• Integers

• Real numbers

• Rational numbers

• Transcendental numbers

Multiple Choice

What is the measure of a central angle in radians if it intercepts an arc with the same length as the radius of the circle?

• 0.5 rad

• 1 rad

• 2 rad

• 3 rad

Multiple Choice

Understanding radian measure, which of the following is true?

• Radian measure is independent of the radius of the circle.

• Radian measure is directly proportional to the diameter of the circle.

• Radian measure is the length of the arc divided by the diameter of the circle.

• Radian measure is the length of the arc divided by the radius of the circle.

Multiple Choice

Why are radians the preferred unit of angle measurement?

• They are easier to calculate with

• They directly relate angles to the length of an arc

• They are universally accepted

• They are more intuitive than degrees

Multiple Choice

Find the arc length of the circle. (Leave answers in terms of $$\pi$$ . Do not round your answer.)

• $$27\pi$$ km

• $$\frac{\pi}{18}$$ km

• $$15\pi$$ km

• $$\frac{45\pi}{2}$$ km

Multiple Choice

If a sector of a circle has an arc length of 8 cm and the central angle is 2 radians, what is the radius of the circle?

• 4 cm

• 8 cm

• 16 cm

• 2 cm

Open Ended

What does the arc length formula tell you about the units involved when measuring angles in Radians?

Multiple Choice

In a right triangle, if the angles are represented as α and β, what is the relationship between these angles?

• α + β = π/2

• α + β = π

• α + β = 2π

• α + β = 0

Open Ended

If the legs are congruent then the base angles are ________________.

Multiple Choice

What is the value of angle α in the triangle shown?

• π/2

• π/4

• π/3

• π/6

Multiple Choice

Using the Pythagorean theorem, what is the value of c in the triangle shown?

• √2

• 1

• 2

• √3

Multiple Choice

What are the values of sin(π/4), cos(π/4), and tan(π/4) after rationalizing and simplifying?

• sin(π/4) = √2/2, cos(π/4) = √2/2, tan(π/4) = 1

• sin(π/4) = 1/√2, cos(π/4) = 1/√2, tan(π/4) = 1

• sin(π/4) = √2, cos(π/4) = √2, tan(π/4) = 1

• sin(π/4) = 1/2, cos(π/4) = 1/2, tan(π/4) = 0

Multiple Choice

What is the measure of angle $$\alpha$$ ?

• $$\frac{\pi}{3}$$

• $$\frac{\pi}{4}$$

• $$\frac{\pi}{6}$$

• $$\pi$$

Multiple Choice

What is the length of side b?

• $$2$$

• $$\sqrt{3}$$

• $$\frac{2}{\sqrt{3}}$$

• $$\frac{\sqrt{3}}{2}$$

Multiple Choice

What are the values of sin(π/6), cos(π/6), and tan(π/6) after rationalizing and simplifying?

• sin(π/6) = 1, cos(π/6) = √3, tan(π/6) = 3

• sin(π/4) = 1/√2, cos(π/4) = 1/√2, tan(π/4) = 1

• sin(π/6) = 1/√3, cos(π/6) = 1, tan(π/6) = 2

• sin(π/6) = 1/2, cos(π/6) = √3/2, tan(π/6) = √3/3

Fill in the Blank

A rectangular pool at Andy's gym measures 25 m by 50 m. How far would Andy swim if he swims across the pool diagonally?

Round to the nearest tenth. Do not include units for this question.

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Poll

How confident do you feel about this topic now?

• Very confident
• Somewhat confident
• Not confident