PRE-CAL 1ST SEMESTER FINAL EXAM REVIEW Name ______

PRE-CAL 1ST SEMESTER FINAL EXAM REVIEW Name ______

CH. 6 Findthe following using. Simplify to lowest terms.

Solve for x.

9. 10. x 11.

x 9

12. The pilot of a helicopter measures the angle of depression to a landing spot to be If the

pilot’s altitude is 1,640 meters, what is the horizontal distance to the landing spot of the

nearest meter?

Convert to degree form. Convert to radian form.

13. 14. = ______ 15. 16. 285° = ______

Find the exact value of the following when the terminal side of angle passes through the point (6, 5).

17. sin = ______18. cos = ______19. tan = ______

Find the exact value of:

20. sin (3) 21. cos( 270°) 22. tan( )

23. sec( ) 24. csc () 25. cot ()

Simplify the given expression.

26. cot x sin x 27. 28. sin 2 t + cot 2 t sin 2 t

CH. 7

If a 0 and b > 0, then each of the functions f(t) = a sin (bt – c) + d and g(t) = acos (bt – c) + d has:

1)Amplitude _____ 2) Period ______3) Phase Shift ______4) Vertical Shift ______

Find the amplitude, period, phase shift and vertical shift of the sine functions graphed below. The

sine functions are graphed over the interval from

5. 6. 7.

Amp: _____ Period: _____ Amp: _____ Period: _____ Amp: _____ Period: _____

P.S. ______V.S.______P.S. ______V.S.______P.S. ______V.S.______

Find the amplitude, period, phase shift and vertical shift of the following functions:

Amplitude: ______Period: ______Phase shift ______Vertical Shift: ______

Identify the amplitude, period, phase shift and vertical shift of the following function. Then graph the function for one complete period.

10. y = 3 sin (2x + ) + 1

amplitude ______period ______

phase shift ______vertical shift ______

11. Write a sine function with the given amplitude, period, phase shift, and vertical shift.

Amplitude: 2; Period: ; Phase shift: ; Vertical shift: ______

12. Write a cosine function with the given amplitude, period, phase shift, and vertical shift

Amplitude: Period: : Phase Shift: Vertical Shift : 4 ______

CH. 8 Find the solutions of each functionwithout your calculator.

1. 2. 3. 4.

5. sin-1(cos 0) 6. cos-1(tan ) 7. tan-1 [tan ()]

Solve each equation graphically.

8. 5sin3x + 6cos3x = 1 9. 2cos2x + sinx + 1 = 0

Solve each equation on the interval

10. 11. 12. 2cosx = 1

CH 9

(Use a sum/difference identity for sine/cosine to find an EXACT value for each trig expression

1. ______

2. ______

3. ______

4. ______

5. tan () = ______

Given , find the exact value of the following:

6. 7. 8.

Given , find the exact value of the following:

9. 10. 11.

Use half angle formulas to find the exact value of each trigonometric function.

12. 13. 14. sin

CH. 10

Use the Law of Cosines or the Law of Sines to solve the triangle.

1. 2.

3. 4.

5. Two trains leave from the same station at the same time. The angle between their two tracks is 120°. One train travels at an average speed of 45 miles per hour and the other at 70 miles per hour. How far apart are the trains after 3 hours?

6. A pole tilts 12° from the vertical, away from the sun, and casts a 34 foot shadow on the ground. The angle of elevation from the end of the shadow to the top of the pole is 64°. How long is the pole?

7. Two surveyors, Sarah and Paul, are 240 meters apart on a riverbank. Each sights a flagpole on the opposite bank. The angle from the pole to Paul (vertex) to Sarah is 63°. The angle from the pole to Sarah (vertex) to Paul is 54°. How far are Sarah and Paul from the pole?

8. Find the area of triangle ABC if b = 24 cm, c = 15 cm, and A = 55°. ______

9. Find the area of triangle ABC if a = 7 ft, b = 11 ft, and c = 14 ft. ______