Exam 1: The Six Trigonometric Functions

Give the reciprocal of the given number. 2x

Give the reciprocal of the given number. 3x ​

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

Find x so the distance between and is

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

Find  if  and θ  terminates in QII.

Simplify the expression  as much as possible after substituting for x .

Simplify the expression  as much as possible after substituting  for x . ​

Suppose the angle formed by the line y = 4 x and the positive x -axis is θ . Find the tangent of θ . ​

Simplify the expression  as much as possible after substituting for x .

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

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

Find the remaining sides of a 30° - 60° - 90° triangle if the side opposite 60° is 9.

The figure shows a walkway with a handrail. Angle α  is the angle between the walkway and the horizontal, while angle  β  is the angle between the vertical posts of the handrail and the walkway. Assume that the vertical posts are perpendicular to the horizontal. Find  α  if  β = 55°. α = __________°

Graph the ordered pair on a rectangular coordinate system: ​

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

Solve for x . a = 2,

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

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

Using your calculator and rounding your answers to the nearest hundredth, find the remaining trigonometric ratios of θ  if sec θ = -1.14 and . sin θ = __________ cos  θ  =  __________ tan  θ  =  __________ cot  θ  =  __________ csc  θ  =  __________