Pre-Calculus A
4.4 Worksheet
Name _________________________________
Date ___________________
Hour ______
TRIGONOMETRIC FUNCTIONS OF ANY ANGLE
1-4 : Determine the exact values of the six trigonometric functions of the angle θ.
2.
1.
3.
4.
5. The point (7, 24) is on the terminal side of an angle in standard position. Determine the exact
values of the six trigonometric functions of the angle.
6-7 : State the quadrant in which θ lies.
6. sin θ < 0 and cos θ < 0
7. sec θ > 0 and cot θ < 0
8-9 : Find the values of the six trigonometric functions of θ.
8. sin θ =
3
5
9. cos θ = –
when θ lies in Quadrant II.
4
5
when θ lies in Quadrant III
10-15 : Evaluate the sine, cosine, and tangent of the angle without using a calculator (no decimals)
10. 225°
11. 300°
13. -495°
14.
5𝜋
3
3𝜋
15.
4
16-19 : Find two solutions of the equation. Give your answers in radians (0 < θ < 2π).
Do not use a calculator.
1
1
√2
√2
𝟏𝟔. 𝒔𝒊𝒏 𝜃 =
𝟏𝟕. 𝒔𝒊𝒏 𝜃 = −
𝟏𝟖. 𝒄𝒐𝒔 𝜃 =
𝟏𝟗. 𝒄𝒐𝒔 𝜃 = −
2
2
2
2
20. Meteorology The monthly normal
temperatures T (in degrees Fahrenheit) for Santa
Fe, New Mexico are given by:
𝜋𝑡
7𝜋
𝑇 = 49.5 + 20.5𝑐𝑜𝑠 ( − )
6
6
Where t is the time in month, with t = 1
corresponding to January. Find the monthly
normal temperature for each month.
a) January
21. Sales A company that produces water skis,
which are seasonal products, forecasts monthly
sales over a two year period to be:
𝜋𝑡
𝑆 = 23.1 + 0.442𝑡 + 4.3 𝑠𝑖𝑛 ( )
6
Where S is measured in thousands of units and t is
the time (in months), with t = 1 representing
January 2006. Estimate sales for each month.
a) January 2006
b) July
b) February 2007
c) December
c) May 2006
22. True or False? Justify your answer without a calculator.
𝑠𝑖𝑛 151° = 𝑠𝑖𝑛 29°
23-27 : Solve the equation. Round your answer to three decimal places, if necessary.
23. 3x – 7 = 14
2
25. 𝑥−1 =
𝑥+2
2
26. 43 – x = 726
27. ln x = -2