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

Name:________________________

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.

4

1. Tan = Find the other 5 trig. functions and the measure of angles and .

6

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

ships?

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 −

4

)

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.

Evaluate:

−1

10. arctan( −1 )

9. sin ( −1 )

11. tan(arccos

3

)

5

12. cot[arcsin(

− 12

)]

13

x

13. sin arctan

2

5.1-5.2

SIMPLIFY

sec 4 x − tan4 x

14.

sec 2 x + tan 2 x

16.

sin 2 x

15.

sec 2 x − 1

tan x sin x

+

csc x tan x

VERIFY

17.

cos x csc x

= tan x

cot 2 x

18.

csc x cot x

−

=1

sin x tan x

1 − cos x

sin x

+

=2

sin 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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