Quiz 4: Trigonometry

sin(a) = √2 / 2 sin(a) = -0.707, approximately Angle a is in quadrant 3. As shown below, angle a is in quadrant 3. What else can be said? According to a calculator, asin(-sqrt(2) / 2 ) = _____ The sine function is negative in quadrants ___ and ___ Quadrant 3 consists of angles greater than __ and less than ___ Angle a = _____ (See Q20 of Quiz4 for diagram)

According to a calculator, asin(-sqrt(2) / 2 ) = -45 ° degrees. The sine function is negative in quadrants 3 and 4 . Angle a is in quadrant 3. Quadrant 3 consists of angles greater than 180 ° and less than 270 °. Angle a = 225 °

Using your calculator and the given triangle height, solve this triangle. Angle A = 29° Angle B = 45° Height (CD) = 2.9 Angle C = Side AC = Side BC = Side AB = (See Q11 of Quiz4 for diagram of non-right triangle cut to form 2 right triangles)

Angle C = 106 ° Side AC = 5.982 Side BC = 4.101 Side AB = 8.132

Using your calculator and the *Law of Sines*, solve this triangle. Angle A = 25° Angle B = 45° Side AB = 8 (See Q10 of Quiz4 for diagram of non-right triangle)

Angle C = 110 ° Side AC = 6.020 Side BC = 3.598

The radius of an arc is 4. The length of the arc is 2. What is the value of angle a? (See Q9 of Quiz4 for diagram)

Angle a = 0.500 radians Angle a = 28.648

Solve for the angle at A and the length BC. Length AC = 6 Angle at C = 50° (See Q7 of Quiz4 for diagram of triangle same as Q5-6)

Angle at A = 40° Length BC = 3.857

Solve for the angle at A and the length AB. Length BC = 4 Length AC = 6 (This is the same right triangle as Q5 with BC as one non-hypotenuse side opposite angle A. AC is the hypotenuse. See Q6 of Quiz4 for diagram)

Angle at A = 41.810º Length AB = 4.472

Solve for the angle at C and the length AB. Length BC = 4 Angle at A = 35º (This is a right triangle and BC is one non-hypotenuse side opposite angle A. AC is the hypotenuse. See Q5 of Quiz4 for diagram)

Angle at C = 55º Length AB = 5.713

cos(θ) = √2 / 2 What are the possible values of the angle theta, in degrees?

Angle theta = 45° or 315°

Which of the following are measures of angles?

Degrees Radians Gradians Right angles Revolutions All of the above.

A radio tower is observed from a point 15 m above ground level (segment AE). The top of the tower is at an elevation of 30º (angle DAC). The base is at an angle of depression of 10º (angle DAB). Find the height of the tower. Height AE = 15 m Height BD = ? Angle BAD = 10º Angle DAC = 30º (See Q14 of Quiz4 for diagram of two right triangles, stacked)

Height BD = 15 m Using a basic trig function: Distance AD = 85 m (rounded to nearest integer) Using a basic trig function: Distance DC = 49 m (rounded to the nearest integer) Total distance from BC = BD + DC = 64 m (rounded to the nearest integer)

Which book of Euclid's Elements contains the definitions of the sine, cosine, and tangent functions? Options: Book 4 Book 5 Book 6 None of the above

None of the above

A planet is known to have a radius (EQ) of 3,000 miles. If the angle at point E is 89.5º, what is the distance from P to M? (See Q12 of Quiz4 for diagram of right triangle with base as radius of a circle)

Segment EP = 3,000 miles Segment PM = 340,779 miles

This is the kind of trig problem required to track distance traveled in an aircraft flying straight and level (The lines AB and CD are parallel.) The highlighted angle at A = 30° The highlighted angle at B = 45° The height at AC = 10 (See Q8 of Quiz4 for diagram)

The angle ABD = 135° The angle ADB = 15° The angle CAD = 60° The angle ADC = 30 ° The length AD = 20 The length AB = 7.321

A right triangle includes an angle of 45° and a hypotenuse of sqrt(2). What is the length of one of the legs of the triangle? (no diagram)

1.0

Which of these is equivalent (or approximately so) to 60° angle? 0.524 radians 0.763 radians 0.926 radians 1.047 radians

1.047 radians

Convert 1.5 right angles to radians.

2.356 radians

Using the following diagram, what is the value of cos(a) in radians? opposite a = 3 adjacent to a = 4 hypotenuse = 5 no angle values given (See Q18 of Quiz4 for diagram of rectangle, cut diagonally to form 2 right triangles)

cos(a) = 0.8 rad

On Saturday, I was working in the yard and noticed this caution warning on my ladder. For a sixteen foot ladder, resting at a 75°, how high will it reach, to three decimal points? Hypotenuse = 16 Height = ? (See Q13 of Quiz4 for diagram of right triangle)

h = 15.455 feet Use the inverse sine function

The Bible says that "the wages of sin is death." What does the sin() function rhyme with? Options: pin pine None of the above.

pine

Using the following diagram, which trig function is equal to 0.6 rad? opposite a = 3 adjacent to a = 4 hypotenuse = 5 no angle values given Options: sin (a) cos (a) tan (a) cot (a) (See Q19 of Quiz4 for same diagram of rectangle as Q18)

sin (a)

Which of these is equivalent to cos(45°)? π/4 sec( 1 / 45°) √2 / 2 1/8 a full circle

√2 / 2 only