Exam 1: The Six Trigonometric Functions

The object shown in the figure is a cube (all edges are equal in length). Suppose the length of the diagonal AH  in the figure is feet. What is the length of edge AB ?

Find the right part of the identity. __________ ​

Write the following in terms of cos  θ  only. cot  θ ​

Multiply.

Multiply. ​

Find csc  θ  if  and . ​

An isosceles triangle is a triangle in which two sides are equal in length. The angle between the two equal sides is called the vertex angle, while the other two angles are called the base angles. If the vertex angle is 60°, what is the measure of the base angles?

Find the right part of the identity.  __________ ​

For points in quadrant IV, the ratio is always negative because x is always positive and y is always negative. In what other quadrant is the ratio always negative?  ​

Write the following in terms of sin  θ  and cos  θ  and then simplify if possible.

Suppose ABC  is a right triangle with C = 90°. If a = 6 and c = 10, find b . ​

Write the following in terms of sin  θ  only. sec  θ ​

Write the following in terms of cos  θ  only. sin θ

Use a ratio identity to find cot  θ  if  and 

Find the remaining sides of a 30° - 60° - 90° triangle if the longest side is 10. ​

If  and θ  terminates in QIII, find cos  θ .

In the diagram below, angle θ  is in standard position. Find , and ​

Find the remaining trigonometric functions of θ  if  and θ  terminates in QII. ​

Solve for x .

Show that the following statement is true by transforming the left side into the right side.