Exam 6: Trigonometric Algebra and Geometry

Evaluate cos(x + y) assuming that . Assume also that x is in the interval and y is in the interval . Give the exact answer.

Evaluate exactly.

For , evaluate each of the following; round your answers to the nearest hundredth. A) cos 2 $\theta$ B) 2cos $\theta$

Find an exact expression for . The following information will be useful:

What is the amplitude of the function ?

-Find the length of both diagonals in a parallelogram that has two sides of length 3, two sides of length 15, and two angles of 33°. Round the answers to the nearest two decimal places.

Evaluate .

-Suppose a = 7 and c = 10. Evaluate u in radians. Round your answer to four decimal places.

Evaluate . Give the exact answer.

What is the period of the function 5sin²(3x)? Give the exact answer.

Evaluate tan(u - v) assuming that . Assume also that u is in the interval and that v is in the interval . Give the exact answer.

-Given a = 14, , . Evaluate: B, b, c Round your answers for b and c to the nearest tenth.

-What is the largest possible area for a triangle that has one side of length 4 units and one side of length 8 units?

Find a formula for:

What angle does the line $y = \frac{4}{11}x$ forms with the horizontal axis. Round the answer to the nearest tenth of a degree.

What is the range of the function ?

Evaluate .

Find the smallest positive number c such that the figure below is part of the graph of the function sin(x + 5c). Give the exact answer.

-Suppose a = 9 and c = 11. Evaluate v in degrees. Round your answer to the nearest hundredth.

-Find the value of b if a = 8 units, v = , and the area of the parallelogram equals square units.