Trigonometry (Radians and Angles)

Fill in the Blanks

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 Blanks

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.

Poll

How confident do you feel about this topic now?

• Very confident
• Somewhat confident
• Not confident