MAT 180 Bergen Community College Trigonometric Functions Test 3 I have sample questions that will be similar to the ones i need completed with the answer. I need all work shown.
Topics of question include:
Radian and Degree Measure
Trigonometric Functions of Any Angle ,
Graphs of Sine and Cosine Functions,
Inverse Trigonometric Functions
, 2Unit Circle
Verifying Trig. Identities
solving trig equations
sum and difference formulas ( sin cosine)
multiple ange formulas MAT 180
Test 3 Study Guide 4.1-5.3
4.1 Co-terminal angles Know how to sketch an angle and find angles that are co-terminal
to a given angle.
4.2 Unit Circle
Know the Unit Circle in both radians and degrees and know the values of the six
trigonometric functions of the common angles on the Unit Circle.
4.3, 4.4, 4.8 Right Triangle Trigonometry
Know how to solve all parts of a right triangle, using Pythagorean Theorem and Sin, Cos
, Tan ratios, and the Law of Sines.
1. Tan = Find the other 5 trig. functions and the measure of angles and .
Know how to use those skills to solve a word problem.
2. Your football has landed at the edge of the roof of a school building. When you are 25
feet from the base of the building the angle of elevation to your football is 21 degrees.
How high off the ground is your football?
3 An observer in a lighthouse 350 feet above sea level observes two ships directly
offshore. The angles of depression to the ships are 4 and 6.5 . How far apart are the
4.5 and 4.6
4. Know how to sketch the graphs of the six trig. functions and transformations.
Sketch (include two full periods).
6. g( x ) = 3 cos( x + )
5. f ( x ) = −4 + sinx
7. f ( x ) = tan( x −
8. f ( x ) = 2 csc x (don’t worry about this)
4.7 Know how to evaluate inverse trig functions and composites involving inverse trig
expressions., including algebraic expressions. You will be asked to give these answers in
EXACT form, meaning good radical form ( no decimals) and angles given in radians in
terms of pi.
10. arctan( −1 )
9. sin ( −1 )
13. sin arctan
sec 4 x − tan4 x
sec 2 x + tan 2 x
sin 2 x
sec 2 x − 1
tan x sin x
csc x tan x
cos x csc x
= tan x
cot 2 x
csc x cot x
sin x tan x
1 − cos x
1 − cos x
19. sin x
5.3 Solve, find ALL solutions
20. cot x + 1 = 0
21. 4sin 2 x − 1 = 0
Additional practice may be found in the Ch review sections
Pg.340:23,33,39,41,43,49,55,65,79,89,91,93 Pg. 392: 9, 13,25,27,31
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