Math Pre Cal Unit 6

Which of the following is not a cofunction​ identity? A. cosθ=sinπ2−θ B. secθ=cosπ2−θ C. tanθ=cotπ2−θ D.

B. secθ=cosπ2−θ

Which of the following is not a fundamental​ identity? A. 1+tan2θ=sec2θ B. cosθ=tanθ/sinθ C. cotθ=1tanθ D.

B. cosθ=tanθ/sinθ

For any real number​ t, if​ P(x,y) is a point on the unit circle corresponding to​ t, then which of the following does not accurately define a trigonometric​ function? A. cost=x B. csct=1y​, y≠0 C. sect=1x​, x≠0 D. cott=yx​, x≠0

D. cott=yx​, x≠0

Which of the following statements is not true concerning radian​ measure? A. An angle in standard position having a radian measure of θ=−11π/6 has a terminal side that lies in Quadrant IV. B. An angle in standard position having a radian measure of θ=−5π/3 has a terminal side that lies in Quadrant I. C. One radian is the measure of a central angle that has an intercepted arc equal in length to the radius of the circle. D. One radian is approximately 57.3°.

A. An angle in standard position having a radian measure of θ=−11π/6 has a terminal side that lies in Quadrant IV.

Which of the following statements best describes the term general​ angles? A. General angles are angles that are not restricted in size and can be either positive​ angles, negative​ angles, or zero. B. General angles are angles whose terminal side lies in Quadrant I. C. General angles are angles that are not acute angles. D. General angles are all angles that are a member of one of the four special families of angles.

A. General angles are angles that are not restricted in size and can be either positive​ angles, negative​ angles, or zero.

Which of the following statements is​ true? A. If θ is an angle belonging to theπ6,π3,π4 ​families, then the reference angle will be π6,π3,π4​, respectively. B. It is not possible for an angle to have the same measure as its reference angle. C. Every angle has a reference angle associated with it. D. For the angle θ=16π6​, the reference angle is θR=π6.

A. If θ is an angle belonging to theπ6,π3,π4 ​families, then the reference angle will be π6,π3,π4​, respectively.

Which of the following statements is not ​true? Choose the correct answer below. A. The expression θ2π(2πr) describes the arc length of a sector of a circle. B. If the central angle of a sector of a circle is θ=5° and the radius of the circle is r=2 ​cm, then the arc length of the sector of the circle is 10 cm. C. The variable s is used to describe the arc length of a sector of a circle. D. The arc length of a sector of a circle is a portion of the circumference of the circle.

B. If the central angle of a sector of a circle is θ=5° and the radius of the circle is r=2 ​cm, then the arc length of the sector of the circle is 10 cm.

Which of the following statements is​ true? A. The length of the hypotenuse of a special π6​, π3​, π2 right triangle is equal to twice the length of the leg opposite the π3 angle. B. The length of the leg opposite the π3 angle of a special π6​, π3​, π2 right triangle is equal to the square root of 3 times the length of the leg opposite the π6 angle. C. It is possible for a special π6​, π3​, π2 right triangle to be isosceles. D. The length of the hypotenuse of a special π6​, π3​, π2 right triangle is equal to the square root of 3 times the length of the leg opposite the π3 angle.

B. The length of the leg opposite the π3 angle of a special π6​, π3​, π2 right triangle is equal to the square root of 3 times the length of the leg opposite the π6 angle.

Which of the following statements best describes two coterminal​ angles? A. Two angles in standard position are coterminal if the terminal sides of both angles lie in the same quadrant. B. Two angles in standard position are coterminal if they have the same terminal side. C. Two angles in standard position are coterminal if they both have the same amount of rotation. D. Two angles in standard position are coterminal if they have the same initial side.

B. Two angles in standard position are coterminal if they have the same terminal side.

Which of the following is not a valid​ equation? A. sin π/4 = cos π/4 B. csc π/ 6 = cos π/3 C. sin π/3 = cos π/6 D. tan π/4 = cot π/4

B. csc π/6 = cos π/3

If the terminal side of an angle θ lies in Quadrant​ III, then which of the following is​ true? A. cscθ<0, cotθ<0 B. tanθ>0, secθ<0 C. sinθ>0, secθ<0 D.

B. tanθ>0, secθ<0

Which of the following statements best describes an angle that is in standard​ position? A. An angle is in standard position if the vertex is at the origin of a rectangular coordinate system and the initial side lies along the positive​ y-axis. B. An angle is in standard position if the vertex is at the origin of a rectangular coordinate system and the initial side lies along the negative ​ x-axis. C. An angle is in standard position if the vertex is at the origin of a rectangular coordinate system and the initial side lies along the positive​ x-axis. D. An angle is in standard position if the vertex is at the origin of a rectangular coordinate system and the initial side lies along the negative​ y-axis.

C. An angle is in standard position if the vertex is at the origin of a rectangular coordinate system and the initial side lies along the positive​ x-axis.

Which of the following statements is not​ true? A. If two triangles are​ similar, then there exists a constant k≥1 which is equal to the ratio of the lengths of corresponding sides. B. The corresponding angles of similar triangles have the same measure. C. Similar triangles have the same shape and size. D. If two triangles are​ similar, then the ratio of the lengths of any two sides of one triangle is equal to the ratio of the lengths of the corresponding sides of the other triangle.

C. Similar triangles have the same shape and size.

Which of the following statements is not ​true? Choose the correct answer below. A. If θ is the central angle of a sector of a circle in​ radians, then the sector represents a portion of the circle equal to θ2π of the entire circle. B. The expression θ2ππr2​, where θ is expressed in​ radians, describes the area of a sector of a circle. C. The area of a sector of a circle is given by the equation A=12θr2​, where θ is an angle given in degrees. D. If the central angle of a sector of a circle is θ=π4​, then the area of the sector of the circle must be 18 of the area of the entire circle.

C. The area of a sector of a circle is given by the equation A=12θr2​, where θ is an angle given in degrees.

Which of the following statements is​ true? A. It is not possible for a special π4​, π4​, π2 right triangle to be isosceles. B. The length of the hypotenuse of a special π4​, π4​, π2 right triangle is equal to twice the length of a leg opposite the π4 angle. C. The length of the leg opposite either of the π4 angles of a special π4​, π4​, π2 right triangle with a hypotenuse of 2 is equal to 1. D. The length of a leg of a special π4​, π4​, π2 right triangle is equal to half of the length of the hypotenuse.

C. The length of the leg opposite either of the π4 angles of a special π4​, π4​, π2 right triangle with a hypotenuse of 2 is equal to 1.

Which of the following statements is not​ true? A. The unit circle is a circle centered at the origin with radius 1. B. The equation of the unit circle is x2+y2=1. C. There are infinitely many points that lie on the graph of the unit circle that have integer coordinates. D. A point​ (a,b) lies on the graph of the unit circle if and only if a2+b2=1.

C. There are infinitely many points that lie on the graph of the unit circle that have integer coordinates.

Which of the following statements is true concerning the conversion between degree and radian​ measure? A. To convert from radians to​ degrees, multiply by 2π and divide by 360 degrees. B. To convert from radians to​ degrees, multiply by π and divide by 180 degrees. C. To convert from radians to​ degrees, multiply by 180 degrees and divide by π. D. To convert from degrees to​ radians, multiply by 180 degrees and divide by π.

C. To convert from radians to​ degrees, multiply by 180 degrees and divide by π.

Suppose that a right triangle has an acute angle θ and side lengths of​ hyp, opp, and adj. Which of the following does not accurately define a trigonometric​ function? A. cscθ=hyp/ opp B. secθ=hyp/ adj C. cotθ=opp/ adj D. sinθ= opp/ hyp

C. cotθ=opp/ adj

Which of the following is not a fundamental​ identity? A. secθ=1cosθ B. cotθ=cosθsinθ C. sec2θ+1=tan2θ D. 1 + cot^2 θ = csc^2 θ

C. sec^2 θ + 1 = tan^2 θ

Which of the following angles does not belong to the π/4 family of​ angles? A. θ=3π12 B. θ=7π4 C. θ=10π4 D. θ=6π/8

C. θ=10π/4

Which of the following statements is not true concerning angle​ measure? A. If an angle has positive​ measure, then the direction of its rotation is counterclockwise. B. If an angle has negative​ measure, then the direction of its rotation is clockwise. C. The angle in standard position formed by rotating the terminal side of an angle one complete counterclockwise rotation has a measure of 360 degrees. D. The angle in standard position formed by rotating the terminal side of angle one complete counterclockwise rotation has a radian measure of π radians.

D. The angle in standard position formed by rotating the terminal side of angle one complete counterclockwise rotation has a radian measure of π radians.