This document provides a set of practice problems for tests in honors algebra 2. There are 13 multiple choice questions testing trigonometric skills like finding trigonometric ratios given angles, using trig identities, and solving right triangles. Students are instructed to show their work elsewhere and only provide the multiple choice answers.

1. NOTE: These self-made testsare usedtohelpyouonyournexttests/quizzesthatcome upinthe future
events.The questionsthatare createdhere are takenfrom lastyear,or evenyearsbefore that.The
numbersusedhere are differentthanthe questions used.Ananswersheetwillbe given,once youdoall
the answershere. Showyourworksomewhere else,all Ineedare the answers. These testsshouldbe
done withoutacalculator,and all answersmustbe solvedinexactvalueswithnodecimals.If youhave
any questionsorneedanyhelp,askme,Mr. Lamkin,Ms. Latham, or any otherpreviousHnrs.Alg2
students.
1) Alex Zhangisin a hotair balloon atan altitude of 75m, and he seeslandingsitesinopposite
directions.The anglesof depressionof the sites are 30° and15° respectively.How farapart are
the sides?
A:_________________________________________
2) Write an expressiontoshowhow the general rotationmatrix isusedtofindthe cos(𝛼 − 𝛽) and
the sin(𝛼 − 𝛽).
A:__________________________________________
3) Considerthe followingequation:
cos89° ∙ cos67° − sin 89° ∙ sin 67° = cos 𝜃
Solve for 𝜃
A:___________________________________________
4) FindALL of 𝜃 so that 0° ≤ 𝜃 ≤ 360°
a) 4cos 𝜃 + √6 + √2 = 0 A:________________________
b) 𝜃 = csc−1 (
2√3
3
) A:________________________
c) 2 + tan 𝜃 = √3 A:________________________
d) 𝜃 = sec−1(−√6 + √2) A:________________________

2. 5) In a 30-60-90 righttriangle,the longerlegof the triangle hasa measuredlengthof √10,what’s
the lengthof the hypotenuse?
A:______________________________________
6) Findthe exactlocationof the point(-4,3) if it’srotated 165°.
A:_____________________________________
7) Findthe followinginexactvalues:
(a) cos
195
2
° A:__________________________
(b) sec 305° A:__________________________
(c) csc 150° A:__________________________
(d) tan 270° A:__________________________
8) Findthe exactvalue of tan 112.5°
A:_____________________________________
9) Giventhat 𝜃 isan acute angle,and sin 𝜃 =
√7
4
, findthe exactvalue of sin 2𝜃.
A:_____________________________________
10) If tan
3
8
, findall possible valuesof:
a) cos 𝜃 A:__________________________
b) sin 𝜃 A:__________________________
11) Findthe exactvalue forsin 97.5
A:______________________________________

3. 12) If cosθ = −
5
6
and 𝜋 ≤ 𝜃 ≤
3𝜋
2
, thenfindthe exactvalue of tan 2𝜃.
A:______________________________________
13) Briana Fengisina car that is travelingonalevel roadtowarda 3-km mountain.The angle of
elevationfromthe carto the top of the mountainchangesfrom15° to 45°. How far has the
car traveled?
A:_______________________________________