Untitled Presentation

Fill in the Blank

Suppose that $$h\left(t\right)\ =\ 5\cos\left(\frac{\pi}{6}t\right)+5$$ represents the periods of high and low tide at a beach. If you want to collect seashells when the tide is at a height of 6.4 feet, what time should you arrive at the beach so the water will not cover the sand? (A graph may help). Round to the nearest tenth.

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Open Ended

Find the sine, cosine, and tangent for the following point on the unit circle. 

(Hint: What is the relationship between coordinates on the unit circle and sine, cosine, and tangent?)

$$\left(\frac{2}{9},\ \frac{\sqrt{77}}{9}\right)$$  

Open Ended

Find the sine, cosine, and tangent for the following point on the unit circle. 

(Hint: What is the relationship between coordinates on the unit circle and sine, cosine, and tangent?)

$$\left(\frac{12}{13},\ \frac{5}{13}\right)$$  

Multiple Select

Given point P is a point that moves along the circumference of the unit circle and θ is the angle formed by the radius OP from the positive x-axis in the counterclockwise direction. It is found that: (a) point P is in quadrant I if 0° < θ < 90°, (b) point P is in quadrant II if 90° < θ < 180°, (c) point P is in quadrant III if 180° < θ < 270°, (d) point P is in quadrant IV if 270° < θ < 360°.

• Point P is in quadrant I if 0° < θ < 90°

• Point P is in quadrant II if 90° < θ < 180°

• Point P is in quadrant III if 180° < θ < 270°

• Point P is in quadrant IV if 270° < θ < 360°

Multiple Choice

What is the reference angle for $$-45^\circ$$ ?

• $$45^\circ$$

• $$135^\circ$$

• $$-45^\circ$$

• $$315^\circ$$

Multiple Choice

What are the relationships between the sine, cosine, and tangent functions in Quadrants II, III, and IV?

• sin θ = +sin(180° - θ)

• cos θ = -cos(180° - θ)

• tan θ = -tan(180° - θ)

• All of the above

Multiple Choice

Determine the quadrant and reference angle for each of the following angles: (a) 138°, (b) 239°, (c) 312°

• Quadrant I

• Quadrant II

• Quadrant III

• Quadrant IV

Multiple Choice

What is the relationship of the trigonometric functions for the following angles? (a) sin 167°, (b) cos 258°, (c) tan 349°

• sin 167° = sin 13°

• cos 258° = -cos 78°

• tan 349° = -tan 11°

• All of the above

Multiple Choice

What is the relationship between sine, cosine, and tangent values with respect to the x and y coordinates for angles in the second, third, and fourth quadrants of the unit circle?

• Sine is the ratio of y to x

• Cosine is the ratio of x to y

• Tangent is the ratio of y to x

• All of the above

Multiple Choice

What are the relationships of sine, cosine, and tangent with respect to the coordinates in the unit circle for the angles in quadrants II, III, and IV?

• sin θ = +y, cos θ = +x, tan θ = +y/x

• sin θ = -y, cos θ = -x, tan θ = -y/x

• sin θ = -y, cos θ = +x, tan θ = -y/x

• sin θ = +y, cos θ = -x, tan θ = +y/x

Multiple Choice

Determine the values of sin θ, cos θ, and tan θ for the angle θ represented in the unit circle diagram.

• sin θ = 0.8829, cos θ = 0.4695, tan θ = 1.8805

• sin θ = -0.5446, cos θ = -0.837, tan θ = 0.6493

• sin θ = 0.5446, cos θ = 0.837, tan θ = 1.6493

• sin θ = 0.8829, cos θ = -0.4695, tan θ = -1.8805

Fill in the Blank

Find the reference angle for an angle measuring -310⁰.

**DO NOT TYPE A DEGREE SYMBOL**

Multiple Choice

Determine the positive or negative signs for sine, cosine, and tangent for angles in quadrants II, III, and IV.

• Positive

• Negative

• Both

• None

Multiple Choice

Determine the value for each of the following based on the reference angle: (a) sin 104° (b) cos 208.2° (c) tan 318°17'

• sin 76°

• 0.9703

• cos 208.2°

• tan 318°17'

Multiple Choice

What is the value of cos(208.2°)?

• -0.8813

• 0.8813

• -0.5

• 0.5

Multiple Choice

Find the reference angle for the following.

• $$\frac{2\pi}{5}$$

• $$-\frac{2\pi}{5}$$

• $$\frac{\pi}{15}$$

• $$\frac{\pi}{5}$$

Multiple Choice

Tanpa menggunakan kalkulator saintifik, tentukan nilai bagi setiap berikut berdasarkan sudut rujukan sepadan. (a) kos 150° (b) tan 225° (c) sin 300°

• kos 150°

• tan 225°

• sin 300°

• semua di atas

Multiple Choice

What is the reference angle?

• 163

• 73

• 27

• 107

Fill in the Blank

Using a calculator, evaluate the $$\tan\ 68\degree$$ . Round your answer to the 4th decimal place.

Fill in the Blank

Find the reference angle for

$$120\degree$$  
(Type the angle with no degree symbol)

Multiple Choice

Which equation would you use to solve for the unknown angle?

• x = sin^–1(4/5)

• x = cos^–1(4/5)

• x = cos^–1(5/4)

• x = tan^–1(4/5)

Multiple Choice

Name the quadrant where tangent is negative and cosine is also negative.

• I
• II
• III
• IV

Fill in the Blank

Using the unit circle, which of the following angles in the first quadrant has its sine value equal to

$$\frac{\sqrt{3}}{2}$$  ? (If it's degrees, write the word degrees after the number, if it's radians, just type the number with no units, also type "pi" for the pi value)

Multiple Choice

Given the triangle QRS, if QS = 8 cm and QR = RS, calculate the value of tan y.

• 0.75

• 0.5

• 0.6

• 0.8

Multiple Choice

Calculate the angle θ and the distance, in cm, between point P and point Q given that the robotic arm has a length of 15 cm and cos θ = -0.866, where 0° ≤ θ ≤ 180°.

• θ = 150°, Distance = 10 cm

• θ = 120°, Distance = 12 cm

• θ = 135°, Distance = 13 cm

• θ = 90°, Distance = 15 cm

Multiple Choice

What is the value of angle θ if cos θ = -0.866?

• 30°

• 150°

• 180°

• 90°

Poll

How confident do you feel about this topic now?

• Very confident
• Somewhat confident
• Not confident