Intro to the unit circle

Dropdown

Sin is related to ​

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, cos is related to ​

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, and tangent is related to ​

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Multiple Choice

According to the complementary rule for right triangle, which of the followings is a true statement?

• sin B = Cos C

• cos A = Sin C

• Sin A = Cos B

• tan A = Cot B

Multiple Choice

Choose the correct set up to find the length of the side x.

• cos(37) = 14/x

• cos(37) = x/14

• tan(37)=x/14

• sin(37)=14/x

Multiple Choice

Determine the value of: tan(C)

• 7 / 24

• 24 / 25

• 7 / 25

• 24 / 7

Multiple Choice

Find the length of side w.

• 21.4 cm
• 18.0 cm
• 36.5 cm
• 43.6 cm

Multiple Choice

Find the measure of the indicated angle.  

• $$6^{\circ}$$

• $$20^{\circ}$$

• $$43^{\circ}$$

• $$47^{\circ}$$

Multiple Choice

The diagram shows a unit circle. State the possible values of a and b.

• $$a=0.9397,\ b=0.3420$$

• $$a=0.9397,\ b=-0.3420$$

• $$a=-0.9397,\ b=0.3420$$

• $$\alpha=-0.9397,\ b=-0.3420$$

​The circle has a center at (0,0) and a radius of 1

Multiple Choice

Find the point on the Unit Circle associated with the angle 5π/3

• (1 / 2 , 1 / 2)

• (-√3 / 2 , 1/2)

• (1 / 2 , -√3 / 2)

• (-√3 / 2 , -1/2)

Multiple Choice

What does the real number t correspond to on the unit circle?

• A point (x, y) on the circle

• The circumference of the circle

• The angle θ

• The radius of the circle

Multiple Choice

Find the point on the Unit Circle associated with the angle 5π/3

• (1 / 2 , 1 / 2)

• (-√3 / 2 , 1/2)

• (1 / 2 , -√3 / 2)

• (-√3 / 2 , -1/2)

Multiple Choice

Evaluate the six trigonometric functions at each real number: a. t = π/6 b. t = 5π/4 c. t = π d. t = -π/3

• t = π/6

• t = 5π/4

• t = π

• t = -π/3

Multiple Choice

What is the exact value?

• -1 / 2
• √3 / 2
• -√3 / 2
• 1 / 2

Open Ended

Use the unit circle to evaluate the following expression exactly.

a) $$\sec\ \frac{2\pi}{3}$$  

b) $$\csc\ \frac{3\pi}{4}$$  

c) $$\ \cot\ 120\degree$$  

d) $$\sec\ \frac{11\pi}{6}$$  

e) $$\csc\ 300\degree$$  

f) $$\cot\ \frac{7\pi}{6}$$  

Multiple Choice

What is the range of the sine and cosine functions as shown in the unit circle?

• -1 to 1

• 0 to 1

• -2 to 2

• -1 to 0

Multiple Choice

What are the ranges of sine and cosine values based on the unit circle?

• -1 to 1

• 0 to 1

• -1 to 0

• -2 to 2

Multiple Choice

What is the definition of a periodic function?

• A function that is constant

• A function that repeats its values at regular intervals

• A function that is always increasing

• A function that has no maximum or minimum

Multiple Choice

What are the even and odd properties of trigonometric functions?

• Cosine and secant are odd

• Sine and cosecant are even

• Cosine and secant are even

• Sine and tangent are odd

Multiple Choice

What is the value of sin(13π/6)?

• 0

• 1/2

• √3/2

• -1/2

Multiple Choice

Evaluate cos(−7π/2) and sin(−t) given that sin(t) = 4/5. What are the values?

• cos(−7π/2) = 0, sin(−t) = −4/5

• cos(−7π/2) = 1, sin(−t) = 4/5

• cos(−7π/2) = −1, sin(−t) = 4/5

• cos(−7π/2) = 0, sin(−t) = 4/5

Poll

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