Math Exam 4

B. SAS

If S represents the length of a known side of an oblique triangle and if A represents the measure of a known​ angle, then which of the following triangles cannot be solved using the Law of​ Sines? A. SAA B. SAS C. SSA D. ASA

D. The graph of r=asinn(O) is a rose with at least one petal having an endpoint lying along the line (O)=0 if n is even.

If a is not equal to 0, and if in a integar, then which of the following statements is not true? A. The graph of r=acosn(O) is a rose with n petals if n is odd. B. The graph of r=asin(o) is a rose with n petals if n is odd. C. The graph of r=acosn(o) is a rose with at least one petal having an endpoint lying along the line (O)=0 if n is even. D. The graph of r=asinn(O) is a rose with at least one petal having an endpoint lying along the line (O)=0 if n is even.

B. r=-asin(O)

If a not equals 0 comma then which of the following polar equations is represented by the graph of a circle whose center does not lie along the line theta=0? A. r=acos(o) B. r=-asin(O) C. r=a D. r=-a

B. the graph is a limacon with an inner loop

If a<0 and b<a, then which of the following statements best describes the graph of r=a+bsin(o)?. A. The graph is a limacon with a dimple. B. The graph is a limacon with an inner loop. C. The graph is a cardioid. D. The graph is a limacon with no inner loop and no dimple

C. (1/2)acsinA

If​ A, B, and C are the measures of the angles of any triangle and if​ a, b, and c are the lengths of the sides opposite the corresponding​ angles, then which of the following expressions does not represent the area of the​ triangle? A. (1/2)bcsinA B. (1/2)acsinB C. (1/2)acsinA D. (1/2)absinC

D. tanA= b/a

In the right triangle provided to the right, suppose that the lengths of sides a and c are known. Also, suppose that the measures of angle A and angle B are known. Which of the following equations cannot be used to determine the length of side b? A. sinB=b/c B. a^2+b^2=c^2 C. cosA=b/c D. tan A=b/a

Square root (s)(s-a)(s-b)(s-c)

Suppose that a triangle has side lengths of​ a, b, and c and suppose that s is the semiperimeter of the triangle. Then which of the following expressions describes the area of the​ triangle?

C. This case could result in a solution where there is no​ triangle, one unique​ triangle, or two unique triangles.

When attempting to solve an oblique triangle given the lengths of two sides and the measure of an angle not included between the two​ sides, which of the following best describes this​ case? A. This case always results in a solution where there is one unique triangle. B. There is no triangle that satisfies the given conditions. C. This case could result in a solution where there is no​ triangle, one unique​ triangle, or two unique triangles. D. This case always results in a solution where there are two unique triangles.

B. The semiperimeter of a triangle is half the sum of the lengths of the three sides of a triangle.

Which of the following best describes the semiperimeter of a​ triangle? Choose the correct answer. A. The semiperimeter of a triangle is the length of the longest side of a triangle. B. The semiperimeter of a triangle is half the sum of the lengths of the three sides of a triangle. C. The semiperimeter of a triangle is the sum of the lengths of the three sides of a triangle. D. The semiperimeter of a triangle is one fourth of the sum of the lengths of the three sides of a triangle.

C. The square of any side of a triangle is equal to the sum of the squares of the remaining two​ sides, minus twice the product of the two remaining sides and the cosine of the angle between them.

Which of the following phrases best describes the Law of​ Cosines? Choose the correct answer. A. The square of any side of a triangle is equal to the sum of the squares of the remaining two​ sides, plus twice the product of the two remaining sides and the cosine of the angle between them. B. The length of a side of a triangle is equal to the sum of the squares of the remaining two​ sides, minus twice the product of the two remaining sides and the cosine of the angle between them. C. The square of any side of a triangle is equal to the sum of the squares of the remaining two​ sides, minus twice the product of the two remaining sides and the cosine of the angle between them. D. The length of a side of a triangle is equal to the sum of the squares of the remaining two​ sides, plus twice the product of the two remaining sides and the cosine of the angle between them.

C. rsin(O)=a

Which of the following polar equations is represented by the graph of a horizontal line for a>0, b>0 and c>0? A. arcos(O)+brsin(O) B. rcos(O)=a C. rsin(O)=a D. r=a

A. The two acute angles of a right triangle are always complementary.

Which of the following statements accurately describes the relationship between the two acute angles of a right triangle? A. The two acute angles of a right triangle are always complementary. B. The two acute angles of a right triangle are always congruent. C. The measures of the two acute angles of a right triangle are always greater than or equal to 45 degrees . D. The two acute angles of a right triangle are always supplementary.

C. An oblique triangle cannot have a right angle.

Which of the following statements best describes an oblique triangle? A. An oblique triangle must have one obtuse angle. B. An oblique triangle cannot have an obtuse angle. C. An oblique triangle cannot have a right angle. D. An oblique triangle must have three acute angles.

B. The graph is a lemniscate. The endpoints of the two loops of the lemniscate occur when theta equals StartFraction pi Over 2 EndFraction and theta equals StartFraction 3 pi Over 2 EndFraction .

Which of the following statements best describes the graph of r^2=a^2cos2(O)? A A. The graph is a lemniscate. The endpoints of the two loops of the lemniscate occur when (O)=0 and (O)=0. B. The graph is a lemniscate. The endpoints of the two loops of the lemniscate occur when theta equals StartFraction pi Over 2 EndFraction and theta equals StartFraction 3 pi Over 2 EndFraction . C. The graph is a lemniscate. The endpoints of the two loops of the lemniscate occur when theta equals StartFraction pi Over 4 EndFraction and theta equals StartFraction 5 pi Over 4 EndFraction . D. The graph is a lemniscate. The endpoints of the two loops of the lemniscate occur when theta equals StartFraction pi Over 3 EndFraction and theta equals StartFraction 4 pi Over 3 EndFraction .

D. If the measures of all three angles of a triangle are​ known, then it is possible to find the area using​ Heron's Formula.

Which of the following statements is not true about finding the area of a​ triangle? Choose the correct answer. A. If the lengths of all three sides of a triangle are​ known, then the most efficient approach for finding the area is to use​ Heron's Formula. B. If the lengths of all three sides of a triangle are​ known, the area can be found by calculating the semiperimeter and using​ Heron's Formula. C. If the lengths of all three sides of a triangle are​ known, then it is possible to find the area using the formula A=(1/2)bcsinA D. If the measures of all three angles of a triangle are​ known, then it is possible to find the area using​ Heron's Formula.

B. In order to find the area of any​ triangle, the lengths of any two sides and the measure of any​ angle, the measure of any two angles and the length of one​ side, or the lengths of three sides of a triangle must be known.

Which of the following statements is true about finding the area of a triangle given that​ A, B, and C are the measures of the​ angles, a,​ b, and c are the lengths of the sides opposite the corresponding​ angles, and h is the length of an​ altitude? A. In order to use the formula Area=(1/2)bh, the triangle must be a right triangle. B. In order to find the area of any​ triangle, the lengths of any two sides and the measure of any​ angle, the measure of any two angles and the length of one​ side, or the lengths of three sides of a triangle must be known. C. In order to use the formula A=(1/2)absinC two sides and the included angle must be given. D. In order to find the area of any​ triangle, the altitude must be given.

B. the measure of two acute angles

Which two given pieces of information are not helpful when trying to solve a right​ triangle? A. The length of the side adjacent to a specific acute angle and the length of the hypotenuse of the right triangle B. The measure of two acute angles C. The length of the side opposite of a specific acute angle and the length of a side adjacent to that same acute angle D. The length of the hypotenuse and the measure of an acute angle