Lesson test: The unit circle and periodic functions

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1.[2p]
On the unit circle, what are $\cos θ$ and $\sin θ$ ?

The $x$ and $y$ coordinates of the point at angle $θ$

Correct

The lengths of the two legs of any right triangle with angle $θ$

The answer is: The $x$ and $y$ coordinates of the point at angle $θ$

The arc length and the sector area at angle $θ$

The answer is: The $x$ and $y$ coordinates of the point at angle $θ$

The slope and the intercept of the ray at angle $θ$

The answer is: The $x$ and $y$ coordinates of the point at angle $θ$

2.[2p]
What is $\sin 150 °$ ?

CorrectNot quite: 0.5

3.[2p]
Convert $150 °$ to radians, to three decimal places.

CorrectNot quite: 2.618

4.[2p]
A sector has radius 6.4 m and angle 0.85 radians. What is its arc length in metres?

CorrectNot quite: 5.44

5.[2p]
A sector has radius 2.5 m and angle 1.2 radians. What is its area in square metres?

CorrectNot quite: 3.75

6.[2p]
Why does $\tan 90 °$ not exist?

Cosine is zero there, and the tangent is the ratio of sine to cosine

Correct

Sine is zero there

The answer is: Cosine is zero there, and the tangent is the ratio of sine to cosine

Because $90 °$ is not an angle of any triangle

The answer is: Cosine is zero there, and the tangent is the ratio of sine to cosine

Because the tangent has period $2 π$

The answer is: Cosine is zero there, and the tangent is the ratio of sine to cosine

7.[3p]
In $y = 3 \sin (2 x) + 5$ , what is the period, to three decimal places?

CorrectNot quite: 3.142

8.[3p]
Which of these are correct identities?

Select all that apply

$\sin^{2} θ + \cos^{2} θ = 1$

Correct

$\cos (- θ) = \cos θ$

Correct

$\sin (π - θ) = \sin θ$

Correct

$\sin (A + B) = \sin A + \sin B$

The answer is: $\sin^{2} θ + \cos^{2} θ = 1$ , $\cos (- θ) = \cos θ$ , $\sin (π - θ) = \sin θ$

9.[3p]
Solve $2 \sin x = 1$ for $0 \leq x < 2 π$ , in increasing order, written in the style "pi/3, 2pi/3".

CorrectNot quite: pi/6, 5pi/6

1.[2p] On the unit circle, what are cosθ and sinθ?

2.[2p] What is sin150°?

3.[2p] Convert 150° to radians, to three decimal places.

4.[2p] A sector has radius 6.4 m and angle 0.85 radians. What is its arc length in metres?

5.[2p] A sector has radius 2.5 m and angle 1.2 radians. What is its area in square metres?

6.[2p] Why does tan90° not exist?

7.[3p] In y=3sin(2x)+5, what is the period, to three decimal places?

8.[3p] Which of these are correct identities?

9.[3p] Solve 2sinx=1 for 0≤x<2π, in increasing order, written in the style "pi/3, 2pi/3".

1.[2p]
On the unit circle, what are $\cos θ$ and $\sin θ$ ?

2.[2p]
What is $\sin 150 °$ ?

3.[2p]
Convert $150 °$ to radians, to three decimal places.

4.[2p]
A sector has radius 6.4 m and angle 0.85 radians. What is its arc length in metres?

5.[2p]
A sector has radius 2.5 m and angle 1.2 radians. What is its area in square metres?

6.[2p]
Why does $\tan 90 °$ not exist?

7.[3p]
In $y = 3 \sin (2 x) + 5$ , what is the period, to three decimal places?

8.[3p]
Which of these are correct identities?

9.[3p]
Solve $2 \sin x = 1$ for $0 \leq x < 2 π$ , in increasing order, written in the style "pi/3, 2pi/3".