Trig Functions

The sine of the complimentary angle to 75°

0.26

y=0.884sin (0.245x-1.093) + 0.400 value of d

0.400

A small plane is 4 miles by land away from the airport. The angle of elevation from the airport to the airplane is 65 degrees. What is the altitude of the plane? Round your answer to the nearest tenth of a mile.

0.5 mile

The cosine of the complimentary angle to 57°

0.84

What is cos(-30)?

0.87

Find the angle with a tangent ratio of 0.9325.

43°

The tide is the regular rising or falling of the ocean's surface. This is due in large part to the gravitational forces of the moon. The following table represents water level of the tide off the coast of Kings Point, N.Y., for a 24 hour period, February 9th through February 10th of 2009. Plot the data points given in the table using hour as the independent variable. Does this data indicate that a sine regression may be appropriate in this case? Explain.

Yes, in the scatterplot the wavelike behavior is apparent although not precise.

If the cotangent and tangent are reciprocals of each other, then what is the cotangent of an angle if the tangent of the same angle is b/a where a and b are not zero?

a/b

In a basic sine curve, where can the zeros NOT be found?

maximum point

The cosine of the complimentary angle to 58°

0.85

The sine of the complimentary angle of 28°

0.88

y=0.884sin (0.245x-1.093) + 0.400 value of c

1.093

A mini toy helicopter ascends 50 feet vertically, then flies horizontally 200 feet. Find the angle of elevation to the helicopter now as seen by an observer at the takeoff point. Round to the nearest degree.

14°

A spruce tree is approximately the shape of a cone with a slant height of 20 ft. The angle formed by the tree with the ground measures 72º. Estimate the height of the tree. Round to the nearest foot.

19 ft

Find cos-1 0.9455 to the nearest degree

19°

Find the angle with a tangent ratio of 0.4877.

26°

A surveyor is standing 550 feet from the base of a redwood tree in the California Redwood Forest. The tree is 362 feet tall. Sketch a drawing that models the situation and then find the angle of elevation of the top of the tree from the spot where the surveyor is standing.

33.4

The average number of customers per day at a home improvement store is given in the following table. Let x represent the day where 1 = Sun of the first week, 7 = Sat of the first week, 8 = Sun of the second week, and 14 = Sat of the second week. Use a graphing calculator to produce a sine regression model for the data. Round a, b, c, and d to the nearest thousandth.

34.081sin(0.888x + 1.341) + 82.822

Find tan-1 1.4826 to the nearest degree.

56°

y=18.614sin (0.521x-1.984) + 76.900 Predict y(14)

61.5

The Sears Tower in Chicago is 1454 feet high. Sketch and find the angle of elevation from a point 750 feet from the base to the top of the tower. Relate your answer to the nearest tenth.

62.7°

Find sin-1 0.9563 to the nearest degree.

73°

Using a scientific calculator or graphing calculator to find the inverse tangent of the ratio. Round to the nearest degree. 9.5

84°

According to the National Weather Service, the average monthly high temperature in the Dallas/Fort Worth, Texas area from the years of 2006-2008 is given by the following table: Let x represent the months and y represent the average maximum monthly temperature. Plot the data on a scatterplot. Choose the plot that best represents the data.

A

What is the domain of a cosine function?

All real numbers

If two triangles are similar, what is true regarding the sides of the two triangles?

They are proportional.

According to the National Weather Service, the average monthly high temperature in the Dallas/Fort Worth, Texas area from the years of 2006-2008 is given by the following table: If the plot was extended to a two year period with 1 = Jan of the first year, 12 = Dec of the first year, 13 = Jan of the second year, 24 = Dec of the second year, describe the plot with the additional information.

Wave-like and repetitive

In a right triangle, which ratio represents the sine of an angle?

opposite:hypotenuse

Which of the following statements is true? Two answers.

sin 18° = cos 72°/sin 72° = cos 18°

Which of the following statements is true? Only one answer.

sin 35° = cos 55°

In right triangle ABC, when angles A and B add up to 90 degrees, what is the cosine of B equal to?

sin A

In the unit circle, the value of sine is the y-coordinate of the unit radius. What is the value of cosine?

x-coordinate