Archive for the ‘Trigonometry’ Category

Problem 1104

Determine whether the statement below is true or false.

The angular speed Ѡ of an object traveling around a circle of radius r is the angle θ (measured in radians) swept out, divide by the elapsed time t.

 

Solution:-

This is the definition of angular speed. The formula used to calculate angular speed is 

Ѡ = \frac{ \theta }{t}.

 

Problem 1103

Complete the sentence below.

An object travels around a circle of radius r with constant speed. If s is the distance traveled in time t around the circle and θ is the central angle (in radius) swept out in time t, then the linear speed of the object is v = ………and the angular speed of the object is Ѡ = ……………….

 

Solution:-

 

An object travels around a circle of radius r with constant speed. If s is the distance traveled in time t around the circle and θ is the central angle (in radius) swept out in time t, then the linear speed of the object is v = \frac{s}{t}and the angular speed of the object is Ѡ = \frac{ \theta }{t}.

 

 

 

 

 

Problem 1102

Complete the sentence below.

On a circle of radius r, a central angle of θ radians subtends an arc of length s = …………..; the area of the sector formed by this angle θ is A = ………………

 

Solution:-

 

On a circle of radius r, a central angle of θ radians subtends an arc of length s = r θ; the area of the sector formed by this angle θ is A = \frac{1}{2} r2 θ.

 

 

Problem 1101

Complete the sentence below.

If the radius of a circle is r and the length of the arc subtended by a central angle is also r, then the measure of the angle is 1 ……………………

 

Solution:-

 

If the radius of a circle is r and the length of the arc subtended by a central angle is also r, then the measure of the angle is 1 radian.

31b

Problem 1100

Complete the sentence below.

A ……………….. is a positive angle whose vertex is the center of a circle.

 

Solution:-

 

A central angle is a positive angle whose vertex is the center of a circle.

 

 

 

Problem 1099

 

Complete the sentence below.

An angle θ is in ……………………….. , ……………………… if its vertex is at the origin of a rectangular coordinate system and its initial side coincides with the positive x-axis.

 

Solution:-

 

An angle θ is in standard position if its vertex is at the origin of a rectangular coordinate system and its initial side coincides with the positive x-axis.

 

 

Problem 1098

Complete the following sentence.

If a particle has a speed of r feet per second and travels a distance d (in feet) in time (in seconds), then d = ………………..

 

Solution:-

 

d = r * t.

 

 

Problem 1097

 

What is the formula for the circumference C of a circle of radius r? What is the formula for area A of a circle of radius r?

 

Solution:-

 

The formula for the circumference C of a circle of radius r is C = 2πr.

The formula for the area A of a circle of radius r is A = πr2.

 

 

Problem 1096

 

Find the cosine of 90°.

 

Solution:-

 

The coordinate at 90° is (0, 1). The cosine represents the x-coordinate of the ordered pair. Therefore, the cosine of 90° is 0.

 

 

Problem 1095

 

Explain the meaning of SOH of the mnemonic device SOH-CAH-TOA.

 

Solution:-

 

The mnemonic device of SOH-CAH-TOA represents the trigonometric ratios for the sine, cosine, and tangent functions. The sine of an angle is equal to the opposite side divided by the hypotenuse.