Trigonometry quarter 1 test

Evaluate and rationalize the denominator when applicable: Sin^2 135 degrees + 3cos 120 degrees

-1

List the possible values of cos⁡θ if θ is a quadrantal angle.

-1, 0, 1

Csc 219.44

-1.574

Find a decimal approximation for the following: cos⁡425∘32′

0.4142

Find a decimal approximation for the following: Tan 753 degrees 24'

0.6594

Evaluate: csc^2 90 + (sin270)(tan180)

1

Sin^2 47 + cos^2 47

1

One angle of a triangle has measure 29∘ and another angle has measure 48∘ . Find the measure of the third angle.

103

Find the measures of two supplementary angles with measures (3z−10)∘ and(2z)∘.

104, 76

One angle of a triangle has measure 21∘37′ and another angle has measure 38∘42′. Find the measure of the third angle.

119 degrees 41'

One angle of a triangle has measure 40∘20′ and another angle has measure 20∘35′. Find the measure of the third angle.

119 degrees 5 minutes

Find an angle in the interval [0∘,90∘) that satisfies the statement. Give answer to the nearest tenth of a degree. Sin0=0.213459

12.3

A radio antenna casts a shadow of 90 ft at the same time that a yard stick casts a shadow of 27 inches. How tall is the antenna?

120

Find the supplement of an angle whose measure is 53 degrees.

127

Evaluate 85 degrees 31 minutes + 42 degrees 53 minutes

128 degrees 24 minutes

The observer deck of a ship is located at the origin of a coordinate system. Find the bearing of a buoy located at the point (8,−8).

135

A water tower casts a shadow of 36 ft at the same time that a 12-in ruler casts a shadow of 3 in. How tall is the water tower?

144

Find the angle of smallest possible positive measure co-terminal with

150

Evaluate: 4sin90+2cos270+3tan0

4

14 degrees 19' 41" + 27 degrees 22' 38"

41 degrees 42' 19"

CotA= 6.3847

8.9

Find the values of csc⁡θ,sec⁡θ,andcot⁡θ for the angle θ in standard position having (4,−2) on its terminal side.

Csc0= - square root of 5, sec0 = square root of 5/2, cot0=-2

Determine which of the following in NOT true:

Csc22< csc 72

Find the values of m and n in the pair of similar triangles

M=10, n=26

Find the values of m and n in the pairs of similar triangles.

M=4, n=5

Evaluate and rationalize the denominator when applicable: sin⁡420∘

Root 3/2

Find the values of sin⁡θ,cos⁡θ,andtan⁡θ for the angle θ in standard position having (−5,12) on its terminal side.

Sin0 = 12/13, cos0 = -5/13, tan0 = -12/5

Tan0=3/5, sec0<0

Sin0= -3 root 34/34, cos0= -5 root 34/34

Find the values of sin⁡θ,cos⁡θ,andtan⁡θ for the angle θ in standard position having (−4,−3) on its terminal side.

Sin0=-3/5, cos =-4/5, tan0=3/4

Determine which of the following is true:

Sin45 degrees + cos45 degrees = tan45 degrees

Determine which of the following is NOT true:

Sin45< sin42

Solve the right triangle. The right angle is at C.

a = 2.3, c = 6.0, A = 22

Solve. The right angle is at C.

b = 32.5, c = 33.4, B = 76.6

Solve. The right angle is at C.

c = 22.8, A = 32.6, B 57.4

Find a decimal approximation for the following: Sec95.29 degrees

-10.846

Evaluate and rationalize the denominator when applicable: 2(csc 210 degrees)(tan 45 degrees) + sec^2 315

-2

Perform the calculation: 53 degrees 46' 38"-31 degrees 51'25"

21 degrees53'13"

A wheel makes 1,314 revolutions per minute. How many revolutions does it make per second?

21.9

A sailboat travels 6 miles on a bearing of 48∘ and then it travels on a bearing 138∘ for 22 miles. How far is the sailboat from its starting position?

23

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. 247∘33′54"

247.57

Give an expression that generates all angles co-terminal with 270∘. Let n represent the integer.

270degrees+nX360degrees

Assume angles are acute angles. Solve for x: tan(x+10) = cot(2x-10)

30

The observer deck of a ship is located at the origin of a coordinate system. Find the bearing of an object located at the point (−5,5).

315

Find the complement of an angle whose measure is 56 degrees.

34

Find a decimal approximation for the following: Sec0= 1.2938

39.4

A water tower casts a shadow of 24 ft at the same time that a 12-in ruler casts a shadow of 6 in. How tall is the water tower?

48

Assume angles are acute angles. Solve for a: sin⁡(4a)=cos⁡(14a)

5

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. 56 degrees 13' 52"

56.23

Convert 70.12∘ to degrees, minutes, and seconds.

70 degrees 7 minutes 12 seconds

A scientist is at a spot that has an angle of elevation of 22.7∘ to the top of the 315 foot tall observatory. How far is the scientist from the base of the observatory?

753

A radio technician is at a spot that has an angle of elevation of 18.5∘ to the top of the 255 foot tall transmitting antenna. How far is the radio technician from the base of the transmitting antenna?

762

The bearing from A to C is N 50∘E. The bearing from C to B is S 40∘E. The bearing from B to A is S 60∘W. If the distance from A to C is 45 miles, what is the distance from C to B?

8

Find an angle in the interval [0∘,90∘) that satisfies the statement. Give answer to the nearest tenth of a degree. Tan0 = 12.34285

85.4

Find the values of sin⁡θ,cos⁡θ,andtan⁡θ for the angle θ in standard position having (−5,12) on its terminal side.

Cos 68 degrees 41'

Determine which of the following is possible:

Cos A = 1/ root 3

Determine which of the following is true:

Sin30 + cos60=tan45

Which of the following has the same absolute value as sin⁡195∘29′?

Sin344 degrees 31 minutes

Find sin⁡A,cos⁡A,tan⁡A for the figure below:

SinA = 12/13, cosA = 5/13, tanA = 12/5

Determine which of the following is undefined

Tan90

Solve. The right angle is at C.

a = 8.2, c = 12.2, B = 48