## College Trigonometry MATH110 Quiz and Final Exams (Reviewer)

Trigonometry is a branch of mathematics that studies triangles, their properties and applications to mathematical and real world problems. Since one of the basic parts of a triangle are its angles, then it will be the subject of the first module of this course.
CAROLINE D.C. JOSE
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### College Trigonometry MATH110 Quiz and Final Exams (Reviewer)

Which angle is coterminal with 150°?
b. 510°

8π radians = ?
d. 4 revs

How many revolutions are in 900°?
d. 2.5

Which of the following radian measures is equal to 300°?
a. 5π/3

How many radians are in 3.5 revolutions?
d. 7π

If the initial side of an angle is at QII and its terminal side got to the third quadrant
by rotating in the counterclockwise direction, then which of the following statements is TRUE about the angle?
a. Its smallest possible measure is less than 180°

Which of the following is the smallest angle measure?
b. 1 degree

What kind of angle is an angle that has an initial side at the positive x-axis and a terminal side at the negative y-axis?
c. Quadrantal

Which of the following angle measure is the largest?
a. 5π/6 Rads

Which of the following degree measures is equivalent to 3π radians?
d. 540°

A and B are coterminal angles. If the measure of B is 910°, then in what quadrant is A located?
c. QIII

What must we do to the degree measure of an angle to convert it to radian measure?
b. Multiply it by π/180

An angle in the standard form has an initial side at the positive x-axis.
True

An angle in the standard position with a measure of –790° is located in which quadrant?
c. QIV

A quadrantal angle is an angle in the standard form and has a terminal side in either axis.
True

Which of the following angle measures is considered special in Trigonometry?
d. π/6

What is the value of cos π/3 + sin π/6?
c. 1

Which of the following has a value of √3/2?
b. sin π/3

What is the value of cos π/6?
b. √3/2

What is the value of cos π-sinπ/2+tanπ/4?
a. -1

The following trigonometric function values are equal to one except for
Select one:
a. csc 90°
b. tan 45°
c. sin 45° (Answer)
d. cos 0°

What angle has equal sine and cosine values?
b. 45°

What is the value of cos π?
c. –1

Which of the following has the largest cosine value? Note: The largest Value of cosine is 1 and minimum value is -1.
a. 10°

How may revolutions are in 810°?
c. 2.25

tan ⁡ π/4 = sin π/2 . Note: tan ⁡ π/4 = 1 and sin π/2 = 1
True

cos ⁡ π/3 - sin ⁡ π/4 + tan ⁡ π/3 =
1-√2+2√3/2

Which of the following angles is not a quadrantal angle?

Select one:
a. 270°
b. 180°
c. 60° (Answer)
d. 90°

sin 0 + cos 0 = 0
Ans: False (note: sin 0 + cos 0 = 1)

cos⁡ π/6 > sin π/6
True

For which of the following angles is the tangent equal to cotangent?
π/4

If the sine of M is positive while its cosine is negative, then in what quadrant is M located?
d. QII

Point H has coordinates (5, –12). What is the value of sec H?
d. 13/5

If sec N > 0 and tan N < 0, then in what quadrant is N located?
c. QIV

Solve (sin x-1)(2cos x-√2)=0
d. {π/2,π/4}

How many values x( where 0≤ x ≤ 2π) will satisfy tan x = 1?
d. 2

Which of the following statements is true about a point K in the fourth quadrant?
b. cot K < 0

The cosine of a point that is in QII is negative.
True

Given P(–4, k), such that tan P > 0. Which of the following statements is FALSE?

Given P(9, –40), determine the value of cos P – sin P
b. 49/41

All six trigonometric function values of a point that is in QI are positive.
True

Which of the following points is a point on the unit circle?
(√10/10, 3√10/10)

The sine of P(0, 12) is 1.
True

Which of the following angles has a terminal side at the second quadrant?
d. 150°

The secant value of an angle can have a value between 0 and 1
False

An angle in the standard position has an initial side on the positive x-axis.
True

Which of the following radian measures is equal to 280°?
14π/9

If the cosecant of M is positive while its cotangent is negative, then in what quadrant is M located?
a. QII

If cos M > 0 and tan M = –7, then in what quadrant is M located?
b. QIV

Which of the following is a solution to the equation 2sin x = –1
7π/6

3π radians = ?
d. 1.5 revs

An angle in the standard form has a negative measure.:
False

All six trigonometric function values of a point that is in QIII are negative.
False

The tangent of a point in the fourth quadrant is positive.
False

The cosecant of a point that is in QIV is negative.
True

Which of the following angle measures is considered special in Trigonometry?
π/4

Point H has coordinates (–8, –15). What is the value of sec H?
-17/8

What is the amplitude of y = –4cos x
a. 4

The period of any sine function is 2π
False

A sine function has infinitely many x-intercepts
True

The amplitude of any cosine function is 1
False

What term refers to the characteristic of the graph of a sine and a cosine function where a specific portion repeats every so often?
d. periodic

Which of the following expressions is equivalent to sin (x – y)?
c. sin x cos y – cos x sin y

Which of the following expressions is equivalent to cos 2B?
d. cos2B – sin2B

What is the period of the graph of y = cos 2x?
a. π

What is the y-intercept of y = sin x?
a. 0

What is the value of csc2 ϴ – 3 – cot2 ϴ?
a. –2

Which of the following expressions has a product of 1?
d. csc ϴ sin ϴ

The function y =sin x is an odd function
True

What is the product (sin ϴ + cos ϴ)( sin ϴ + cos ϴ)?
1+2sin ϴ cos ϴ

Which of the following is the reciprocal of sec ϴ?
b. cos ϴ

A sine function is a periodic function
True

The y-intercept of y = sin x is 1
False

A cosine function has only one y-intercept
True

The reciprocal of tangent is cotangent
True

sec2ϴ + tan2ϴ = 1
False

Convert sin 5π + sin 3π to product form.
c. 2 sin⁡4π cos⁡π

What trigonometric function is equal to the ratio of the hypotenuse to the adjacent leg?
a. secant

Which of the following fractions is equal to the tangent of an angle?
opposite leg/adjacent leg

Which of the following fractions is equal to the cosecant of an angle?
opposite/adjacent

The tangent of an angle is never greater than 1.
False

The sum of the measures of the two acute angles in a right triangle is always equal to 90.
True

In right ∆ABC, sec A = ?
13/12

Which of the following trigonometric ratios do not involve the adjacent leg?
c. sine

Solve the right triangle below.
a. x = 30, mA = 28.07°, mB = 61.93°

In which of the following cases is the Law of Sines always applicable?
c. SAA

Which of the following is the Law of Sines?
a/sinA=b/sinB=c/sinC

The Law of Sines can be used to solve a triangle where all three sides are known.
False

In an ASA case, the endpoints of the given side are the vertices of the two given angles.
True

A triangle can be solved given the measures of all of its angles.
False

In right ∆ABC, sin A = ?
5/13
*note: IF Right angle is B then sin A = opposite over hypotenuse = a/b
IF RIght angle is C then sin A = a/c

If sec ϴ =17/8, then what is x?
a. 85

A 13-feet ladder is placed on a vertical wall such that the top of the ladder is 12 feet high up the wall. How far is the foot of the ladder from the wall?
b. 5 feet

If we apply the Pythagorean theorem in the right triangle below, then what equation can we form?
c. b^2 + c^2 = a^2

A right triangle can be solved if the only known measure is that of a leg.
False

The sine of an angle is never greater than 1.
True

The sum of the measures of the two acute angles in a right triangle is always equal to 90.
True

What expression gives the hypotenuse h of the triangle below?
12/cos 20

Which of the following fractions is equal to the cosecant of an angle?
hypotenuse/oppsite leg
*note: In a right triangle, the cosecant of an angle is the length of the hypotenuse divided by the length of the opposite side.

What trigonometric function is equal to the ratio of the adjacent leg to the opposite leg?
d. cotangent

Using the right triangle below, what is cos B – sec A + tan B?
41/60

If we apply the Pythagorean theorem in the right triangle below, then what expression solves for the value of b?
√a^2+c^2

If cot θ = 11/17, then what is x?
a. 300

If the equation p sin⁡D=m sin⁡L is an expression of the Law of Sines, then which of the following statements must be TRUE?
b. The length of the side opposite angle D is m.

Which o the following expressions is equivalent to
1/2[cos 3π-cos 11π]?
c. sin 7π sin 4π

Which of the following is equivalent to cos x cos y?
cosX cosY = (1/2) [ cos (X - Y) + cos (X + Y) ]

A triangle with sides of 8, 10 and 2√41 is a right triangle.
True

Solve 2csc x – 4 = 0 (where 0 ≤ x < 2π)
{π/6, 5π/6}

Using the right triangle below, what is sin B – csc A + tan B? A=8 B=6 C=empty
1/10

Convert cos π/5 + sin π/7 to product form.
a. 2 sin 6π/35 cos 2π/35

The sides of a triangle have measures 7, 13 and 10. What is the measure of the angle opposite the side with a measure of 7?
a. 32.20°

The solutions to 2sin x + 1 = 0 are on the first and second quadrants.
False

The sine of an angle is never negative.
False

The ratio of the hypotenuse to the opposite leg is called the cosecant.
True

Which of the following trigonometric ratios do not involve the opposite leg?
a. secant

In right ∆MPL, sec M = ?
L=9, P=41, M=40
Ans: 41/9

Which of the following equations is a result of the application of the Law of Sines on the triangle below?
a. m sin⁡L=r sin⁡C

If all three angles of a triangle are known, then the measure of any side can be determined.
False

A triangle can be solved using the Law of Cosines if the measure of two of its angles and an included side are given.
False

Which of the following fractions is equal to the cotangent of an angle?
adjacent leg/opposite leg

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