trig unit 1

What is the degree measure of -π/8 radians?

- 22.5º

Which of the following angles is coterminal with 55º?

- 305º

Which of the following angles is coterminal with - 40º?

- 400º

Find the linear speed, in centimeters per second, of the tip of the second hand of a round watch with the length of 1.5 cm.

0.157 cm/s

Transformations can be performed in any order.

False

Find the point (x,y) on the unit circle that corresponds to the angle 2π/3

(-1/2, √3/2)

Find the point (x,y) on the unit circle that corresponds to the angle 3π/4

(-√2/2, √2/2)

Find the point (x,y) on the unit circle that corresponds to the angle -3π/2

(0,1)

A hiker is walking towards a straight road when he encounters a marsh. He turns 60º to the left and walks 2 miles in that direction to reach the road. how far is the point where he reaches the road from the point where he would reach the road if the was no such marsh?

1.73 miles

Find the approximate degree measure of the central angle of a circle with the radius of 10 cm that intercepts an arc with the length of 2 cm

11.5º

Find the approximate degree measure of the central angle of a circle with the radius of 10 cm that intercepts an arc with the length of 2 cm.

11.5º

From a highway above the train tracks, the angle of depression of the oncoming train is measured to be 15º. If the highway is 30 meters above the tracks, what is the distance from the train to the point directly below the highway?

112 meters

The area of the sector of the circle with the radius of 5 inches is 25 square inches. Find the approximate degree measure of the central angle of the sector of this circle.

114.6º

An angle with radian measure of 11π/3 is coterminal with angle

17π/3

Bill and Nina are on the merry-go-round. Bill is twice as far away from the center as Nina. The ratio of Bill's angular speed to Nina's is

1:1

What is the degree measure of 7π/36 radians?

35º

An angle with radian measure of -π/5 radians lies in quadrant

4

A Ferris Wheel takes 15 minutes to make one revolution. If its radius is 100 feet, what is the linear speed of the person riding the wheel?

41.9 ft./min

A bicycle wheel makes 100 revolutions per minute. If the diameter of the wheel is 25 inches, what the linear speed of a point on the tire?

7850 inches/minute

If a circular pizza is diagonally cut into 10 slices, the area of each slice is 7.5 square inches. Find the approximate diameter of the pizza.

9.8 in

In which of the following lists are all angles coterminal?

90º, 450º, 810º

A triangle can be solved if one side and one acute angle are known.

False

All points on a rotating disc have the same linear speed.

False

An angle of 2 radians is generated by one complete revolution of the terminal side of the angle around its vertex.

False

An angular speed of 1 revolution per second is equivalent to 1 radian per second

False

Tangent of an acute angle of a right triangle is always less than one.

False

The area of a sector of a circle is proportional to the radius of the circle.

False

The area of a sector of the unit circle equals the radian measure of the central angle of this sector

False

The area of a sector of the unit circle equals the radian measure of the central angle of this sector.

False

The cosecant of an angle is defined as the reciprocal of the x-coordinate of the corresponding point on the unit circle

False

The cotangent of real number 0 is 0

False

The degree measure of an angle cannot exceed 360º.

False

The degree measure of an angle is determined by the length of its rays.

False

The domain of cotangent function is all real numbers

False

The term "angle of depression" is used for the objects that lie above the horizontal.

False

The terminal side of 450º angle coincides with the positive x-axis

False

The terminal side of the angle with the radian measure of 19ππ/2 coincides with the positive half of the y-axis

False

The terminal sides of 150º angle and -60º angle lie on the same line

False

The terminal sides of 150º angle and -60º angle lie on the same line.

False

A central angle of one radian in a unit circle intercepts an arc of length 1

True

An angle of 1 radian is approximately equivalent to 57 1º angles

True

If a right triangle has acute angles of 30º and 60º, then the lengths of its sides have the ratio 1:√3 :2

True

If the sides of a triangle satisfy the Pythagorean Theorem, then one of the angles of the triangle is 90º.

True

Sine of an acute angle of a right triangle is always less than one

True

The area of the sector of the circle with the central angle of 1 radian is approximately one-sixth of the area of the circle.

True

The cosine of 300º angle is the same as the cosine of 60º.

True

The range of cosine function is [-1, 1].

True

The secant of π/2 is undefined

True

The sine of an angle is defined as the y-coordinate of the corresponding point on the unit circle

True

The tangent of real number π is 0

True

The terminal side of the angle with the radian measure of 11π11π coincides with the negative half of the x axis

True

The terminal side of the angle with the radian measure of 11π11π coincides with the negative half of the x axis.

True

Which of the following sets, expressed in interval notation, is the range of the function y=x^4 +3?

[3,∞)

find the cotangent of the angle -π

undefined

The angular speed, in radians per seconds, of a second hand of a clock is

π/30

Use period and symmetry of the trigonometric functions to evaluate cos (-9π/4)

√2/2

Use period and symmetry of the trigonometric functions to evaluate cos(-315º).

√2/2

What is cot (4π/3)

√3/3